IEP goals for order of operations and exponents
By the IEP Atlas editorial teamLast updated
Short answer
An order of operations IEP goal names the kind of expressions, asks the student to show each step, and sets a criterion from the baseline. Example: given 10 expressions with up to four operations, parentheses and one exponent, the student will rewrite the expression after each step and reach the correct value for 8 of 10, up from 3 of 10.
Order of operations errors look like carelessness, but they are usually a rule learned wrong. The student who works 12 minus 4 plus 3 and gets 5 is applying PEMDAS literally: addition comes before subtraction in the word, so add first. A goal that only counts right answers will not catch that. A goal that asks the student to show each step will.
The 12 goals below cover the order of operations, exponents and the algebra skills that depend on them. Each shows the condition, the behavior, a criterion with its denominator, an illustrative baseline and a link to the full template. The numbers are illustrations, not benchmarks. For other math areas, start with the math IEP goals pillar.
Why order of operations goals fail
Three patterns cause most of the errors teams see on probes:
- Left-to-right trouble. Multiplication and division are one step, done left to right. So are addition and subtraction. The mnemonic hides this, so students divide after multiplying even when the division comes first.
- Exponent as multiplication. The student reads 3 squared as 3 times 2 and writes 6.
- Losing the line. The student does three steps in their head and drops a number. Rewriting the whole expression after each step prevents most of these slips.
The federal algebra practice guide recommends teaching students to notice the structure of expressions and to study solved problems, including ones with errors.[1] Goals that ask the student to rewrite one step at a time, or to find the error in a worked problem, put that advice into the IEP.
How to choose the right goal
Give 10 expressions and code each wrong answer by its first error.
| Most common first error | Sub-skill | Measure |
|---|---|---|
| Adds before subtracting, multiplies before dividing | Left-to-right within a level | Expressions correct out of 10 |
| Ignores parentheses or brackets | Grouping symbols | Expressions correct out of 12 |
| 3 squared written as 6 | Exponent meaning | Items correct out of 10 |
| Right order, arithmetic slip | Computation (allow a calculator for the arithmetic) | Expressions correct out of 10 |
| Correct answers, cannot say why | Explaining a step | Rubric points |
| Errors only when variables appear | Evaluating and simplifying expressions | Items correct out of 10 |
If basic facts slow every step, let the student use a calculator for single operations only, not for the whole expression. That keeps the goal about order.
Goals for the order of operations
- Whole numbers, one step per line: Given 10 expressions with up to four operations and parentheses, the student will rewrite the expression one step at a time and write the correct value for 8 of 10 on 3 consecutive probes. Baseline: 3 of 10. Template
- With one exponent: Given 10 expressions with 3 to 4 operations, parentheses and one exponent, the student will underline the first operation at each step and reach the correct value for 8 of 10. Baseline: 3 of 10. Template
- Nested grouping: Given 12 expressions with nested parentheses and brackets, exponents and a fraction bar, the student will work from the innermost group out and solve 10 of 12. Baseline: 5 of 12. Template
- Explaining an error: Given a worked expression with one order of operations error, the student will name the wrong step, state the rule and rework it, scoring 5 of 6 rubric points on 3 of 4 samples. Baseline: 2 of 6. Template
Weak: "The student will use PEMDAS with 80% accuracy." Measurable: the one-step-per-line goal, which names the expressions and makes each step visible.
Goals for exponents and roots
- Squares and cubes: Given 10 expressions with whole-number bases and exponents of 2 or 3, the student will write the value of 9 of 10 on 2 consecutive probes. Baseline: 3 of 10. Template
- Three forms: Given 10 items mixing repeated multiplication, exponent form and standard form, the student will convert each to the other forms for 8 of 10. Baseline: 3 of 10. Template
- Exponent rules: Given 10 monomials using the product, quotient and power rules, the student will simplify and name the rule used for 8 of 10. Baseline: 2 of 10. Template
- Square and cube roots: Given 20 root items with perfect squares to 225 and perfect cubes to 125, the student will write the root and check it by multiplying for 17 of 20. Baseline: 7 of 20. Template
Weak: "The student will understand exponents." Measurable: the three forms goal, which asks the student to show that 2 to the 4th means 2 times 2 times 2 times 2, which equals 16.
Goals for order of operations in algebra
- Distributive property: Given 10 expressions such as 4(x plus 3) minus 2x, the student will expand and simplify 8 of 10. Baseline: 2 of 10. Template
- Evaluating a function: Given 10 functions and an input, such as f(x) = 2x squared minus 5 for x = 3, the student will evaluate 9 of 10 correctly. Baseline: 4 of 10. Template
- Checking a solution: Given 10 equations with a proposed value, the student will substitute, simplify in order and decide whether it is a solution for 9 of 10. Baseline: 5 of 10. Template
- Finding errors in solved equations: Given 6 solved equations with one error each, the student will find the error and fix it, scoring 10 of 12 rubric points. Baseline: 4 of 12. Template
Weak: "The student will evaluate expressions." Measurable: the function goal, which gives an example of the item type and a criterion with its denominator.
How to measure order of operations goals
Score percent accuracy on a fixed set, but record the step where each wrong item first broke. Probe weekly with new numbers and the same structure: for example, 3 items with parentheses, 3 with an exponent and 4 with mixed levels. Short weekly probes graphed over time are how a team decides whether to keep the current approach.[2]
Filled-in example for the one-step-per-line goal on the accuracy data sheet:
| Date | Correct out of 10 | First error, most common | Steps shown | Notes |
|---|---|---|---|---|
| Jan 9 | 3 | Added before subtracting | 2 of 10 | Baseline 1 |
| Jan 16 | 2 | Same | 1 of 10 | Baseline 2 |
| Jan 23 | 4 | Same | 3 of 10 | Baseline 3, median 3 |
| Jan 30 | 5 | Exponent as multiplication | 10 of 10 | Rewrote each line |
| Feb 6 | 7 | One arithmetic slip | 10 of 10 | |
| Feb 13 | 7 | Division before multiplication when left of it | 10 of 10 | Reteach left to right |
The "steps shown" column jumped before the score did. That is the order you want: the habit first, then accuracy.
| Goal type | Method | Data sheet | How often |
|---|---|---|---|
| Expressions and exponents | Percent accuracy | Accuracy data sheet | Weekly |
| Explaining errors | Rubric points | Rubric scoring data sheet | Every 2 weeks |
Short-term objectives
For the expression goal with one exponent:
- By the first report, given 10 expressions with two operations at different levels and no exponents, the student will solve 7 of 10 showing each step.
- By the second report, given expressions with parentheses and two levels, the student will solve 7 of 10.
- By the annual review, given expressions with up to four operations, parentheses and one exponent, the student will solve 8 of 10.
Adapting by grade band
| Grade band | Typical expressions | Supports | Example criterion |
|---|---|---|---|
| Grade 5 | Two operations, parentheses, whole numbers | Step card | 8 of 10 |
| Grades 6 to 8 | Exponents, brackets, fraction bars, integers | Step card, calculator for single operations | 10 of 12 |
| High school | Expressions with variables, functions, roots | Formula sheet | 9 of 10 |
For the wider algebra goal set, see IEP goals for high school math and the algebra goals page, including middle school algebra goals. Integer computation, which trips up many order of operations items, is in the math calculation goals. Run each draft through the goal checker.
Frequently asked questions
Should I teach PEMDAS to students with IEPs?
Teach the levels, not just the word. Many teams draw four rows: grouping, exponents, multiplication and division together, then addition and subtraction together, each done left to right. Students who learned PEMDAS letter by letter often add before subtracting because A comes before S.
Can a student use a calculator on an order of operations goal?
Allow it for single operations if facts slow the student down, and say so in the condition. Do not allow a calculator to evaluate the whole expression, because many calculators apply the order for the student and the goal would no longer measure the skill.
How many expressions should an order of operations probe include?
Ten is enough for most goals and takes about 10 to 15 minutes. Keep the mix the same every week, such as 3 with parentheses, 3 with an exponent and 4 with mixed levels, so scores can be compared.
Use it in IEP Atlas
- Algebra goals (math)
- Middle school algebra goals
- Math IEP goals
- Percent accuracy measurement guide
- IEP goal checker
Related guides
- IEP goals for math: calculation, problem solving and functional math
- IEP goals for high school math (algebra and beyond)
- IEP goals for math calculation
- Functional math IEP goal examples for high school
Sources
- Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students, What Works Clearinghouse, Institute of Education Sciences
- Progress Monitoring: Data & Goal Setting, National Center on Intensive Intervention
Written and checked by the IEP Atlas editorial team under our editorial policy. This guide describes general practice and federal rules. It is not legal advice; your state may add requirements, and the IEP team makes the decisions for each student.