IEP goals for math concepts and applications
By the IEP Atlas editorial teamLast updated
Short answer
A math concepts and applications IEP goal measures whether the student understands what numbers mean and can use them, not just compute. Example: given 10 fractions between 0 and 2 and number lines marked only at whole numbers, the student will place 8 of 10 correctly on 3 weekly probes, up from 3 of 10.
"Concepts and applications" is the half of math that computation probes miss. It covers number meaning (where 0.4 sits on a number line, whether 3/8 is more than a half), reading data, and using math in a real task such as finding 20% off a price. Many achievement tests report it as a separate score, and many students with IEPs show a wider gap here than in calculation.
The 12 goals below are grouped into four areas. Each names the condition, behavior and criterion, shows an illustrative baseline and links to its template. The numbers show the shape of a goal, not a benchmark. For the full set of math goals, start with the math IEP goals pillar.
How concepts goals differ from calculation goals
A calculation goal asks for an answer to a bare problem. A concepts goal asks the student to show what a number or operation means: place it, compare it, model it or explain it. An applications goal asks the student to use that meaning in a context, such as a graph, a recipe or a sale sign.
The difference matters when you write the criterion. A student can score 9 of 10 on fraction addition by following a rule while placing 1/2 to the right of 3/4 on a number line. Federal intervention guidance recommends visual representations such as number lines for exactly this reason: they show whether the student understands magnitude.[2] The fractions practice guide makes the number line central to fraction instruction for the same reason.[3]
How to choose the right concepts goal
Give a short mixed probe of 12 to 16 items across the areas below and look for the area with the most errors. Then pick one sub-skill, not three.
| Student profile | Sub-skill | Measure |
|---|---|---|
| Computes well, cannot estimate or spot an absurd answer | Number line placement, rounding | Items within a set distance, out of 10 |
| Follows fraction rules, cannot say which fraction is bigger | Fraction magnitude and equivalence | Pairs correct out of 10 |
| Reads a graph title but not the axes | Reading data displays | Questions correct out of 10 |
| Sets up percent problems wrong in context | Percent and ratio applications | Problems correct out of 10 |
| Explains nothing, answers by guess | Explaining with a model | Rubric points |
If word problem setup is the main problem, a problem solving goal is a better fit. Concepts goals work best for the meaning underneath.
Goals for number concepts
- Number line estimation: Given 10 numbers to place on an empty 0 to 100 number line marked only at the ends, the student will mark 7 of 10 within 5 units of the correct spot on 3 consecutive probes. Baseline: 3 of 10. Template
- Comparing whole numbers: Given 20 pairs of two- and three-digit numbers, the student will write the correct symbol (less than, greater than, equal) for 18 of 20 pairs. Baseline: 11 of 20. Template
- Rounding: Given 10 whole numbers within 10,000 and a stated place, the student will round 8 of 10 correctly on 2 of 3 weekly probes. Baseline: 4 of 10. Template
Weak: "The student will improve number sense." Measurable: the number line goal, which names the range, the tolerance and the count.
Goals for fraction concepts
- Fractions on a number line: Given 10 fractions between 0 and 2 and number lines marked only at whole numbers, the student will place 8 of 10 correctly on 3 weekly probes. Baseline: 3 of 10. Template
- Comparing fractions: Given 10 pairs of fractions with unlike numerators and denominators, the student will compare 8 of 10 correctly and name the strategy used (benchmark, common denominator or model). Baseline: 4 of 10. Template
- Equivalent fractions: When given a fraction with a denominator of 2, 3, 4 or 6, the student will generate an equivalent fraction with a model on 6 of 8 opportunities across 2 sessions. Baseline: 2 of 8. Template
Weak: "The student will understand fractions." Measurable: the comparing fractions goal, which says what kind of pairs and how the student shows the reasoning.
Goals for data and graphs
- Reading bar and picture graphs: Given a bar graph and 10 questions about it (most, least, how many more), the student will answer 8 of 10 correctly on 3 of 4 probes. Baseline: 4 of 10. Template
- Reading tables and charts: Given a table or schedule and 10 questions, the student will find the information and answer 9 of 10. Baseline: 5 of 10. Template
- Mean, median, mode and range: Given 5 data sets of 6 to 10 numbers, the student will find the 4 measures for each and score 16 of 20 measures correct. Baseline: 6 of 20. Template
Weak: "The student will interpret data." Measurable: the table goal, which gives the display, the question count and the criterion.
Goals for applying math in context
- Percent of a number: Given 10 discount, tax or tip problems and a calculator, the student will find the percent of the amount for 8 of 10 on 2 consecutive probes. Baseline: 2 of 10. Template
- Proportions: Given 10 proportions with one missing value and whole-number answers, the student will solve 8 of 10 correctly. Baseline: 3 of 10. Template
- Reasonable measures: Given 10 everyday objects, each with three possible measures, the student will choose the reasonable measure for 9 of 10 (for example, a door is about 7 feet, not 7 inches). Baseline: 5 of 10. Template
Weak: "The student will apply math to real situations." Measurable: the percent goal, which names the contexts, the tool and the set size.
How to measure concepts and applications goals
Use percent accuracy on a fixed set of 10 items, with new numbers on each form. Probe every week or every other week. Brief probes graphed over time are how a team sees whether progress is on track.[4] For number line goals, decide the tolerance before the baseline: within 5 on a 0 to 100 line, or within 1/8 of a whole on a 0 to 2 fraction line.
Here is a filled-in accuracy data sheet for the fractions on a number line goal:
| Date | Correct out of 10 | Percent | Error pattern | Support |
|---|---|---|---|---|
| Sep 12 | 3 | 30% | Placed by numerator only (3/4 at 3) | None |
| Sep 19 | 2 | 20% | Same | None |
| Sep 26 | 3 | 30% | Same, median baseline 3 | None |
| Oct 3 | 5 | 50% | Fractions over 1 still wrong | Fraction strips nearby |
| Oct 10 | 6 | 60% | Improper fractions only | Strips nearby |
| Oct 17 | 6 | 60% | One sixths error | No strips |
| Goal type | Method | Data sheet | How often |
|---|---|---|---|
| Number line, comparing, fractions, data | Percent accuracy | Accuracy data sheet | Weekly |
| Equivalent fractions with models | Opportunities | Opportunity data sheet | 2 times a week |
| Explaining a comparison | Rubric points | Rubric scoring data sheet | Every 2 weeks |
Short-term objectives for concepts goals
Step by number range or by support. For the fractions on a number line goal:
- By the first report, given fractions between 0 and 1 with denominators 2 and 4, the student will place 7 of 10.
- By the second report, given fractions between 0 and 1 with denominators to 8, the student will place 7 of 10.
- By the annual review, given fractions between 0 and 2, including improper fractions, the student will place 8 of 10.
Adapting concepts goals by grade band
| Grade band | Typical concept | Typical application | Example criterion |
|---|---|---|---|
| K to 2 | Comparing numbers, number line to 20 | Picture graphs, measuring with cubes | 8 of 10 items |
| Grades 3 to 5 | Fractions on a number line, rounding | Bar graphs, line plots, elapsed time | 8 of 10 pairs |
| Middle school | Rational numbers, ratio | Percents, mean and median | 16 of 20 measures |
| High school | Proportional reasoning | Budgets, pay stubs, unit price | 9 of 10 with a calculator |
For grade-level templates, see grades 3 to 5 math goals and middle school math goals. The full sets live on the fractions goals and data, graphs and patterns goals pages. Run each draft through the goal checker before the meeting.
Frequently asked questions
What does math concepts and applications mean on an IEP?
It means understanding what numbers and operations represent and using that understanding in context: placing numbers on a number line, comparing fractions, reading graphs and solving percent or measurement tasks. It is usually scored separately from calculation on achievement tests.
Can one goal cover both calculation and concepts?
It is better to write two. A combined goal hides which part is improving. If the team only has room for one, choose the area where the student's errors are most frequent and keep the probe focused on it.
How do I score a number line goal fairly?
Set a tolerance before the baseline and write it on the data sheet, such as within 5 on a 0 to 100 line. Use a clear ruler overlay so every scorer measures the same way. Count an item correct only if the mark falls inside the tolerance.
Use it in IEP Atlas
- Math IEP goals
- Fractions goals (math)
- Data, graphs and patterns goals (math)
- Number sense goals (math)
- Percent accuracy measurement guide
- IEP goal checker
Related guides
- IEP goals for math: calculation, problem solving and functional math
- IEP goals for math calculation
- Math problem solving IEP goal examples
- IEP goals for decimals and percent
- Math vocabulary IEP goals
Sources
- 34 CFR §300.320: Definition of individualized education program, Legal Information Institute, Cornell Law School
- Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades, What Works Clearinghouse, Institute of Education Sciences
- Developing Effective Fractions Instruction for Kindergarten Through 8th Grade, 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.