Math goals are often tricky to line up with the Common Core Standards (which aren’t endorsed by the department of Ed anymore but are still used by almost every curriculum). Meeting a low skill level to an upper grade level can take a lot of thought. Hopefully these examples can give you some new ideas, get you thinking about new ways to track, and if they are written well, they should lead you to progress monitoring.

A question I hear a lot is: How can I use standards that are often too advanced for grade level students, to guide my students who are below grade level? My first thought is to take only the meat of the standards. Many textbooks create math problems that are “interpretations” of the standards. However, when you get to the meat of the standard, there is one or two key skills that students can learn. It’s okay if students can’t do every aspect of the standard. If they can access the basic skill, or one aspect of the content, that is still grade level content AND is differentiating.

There’s a common misconception that if a student receives a goal on grade level, that they no longer need services. This is not true if the IEP goals are creating a way to access grade level standards through differentiating and narrowing down content. I am always a proponent of getting students in special education as much grade level content as possible. So to wrap this up, look for narrowing down the standards to a specific skill that can be taught. Talk with general education teachers to help guide you to which skills are most important. And of course, look at their testing to see which skill areas they are deficient in. Sometimes I write a goal that is skill specific and then another that is grade specific (but still under their area of weakness). Other times, I write them together.

## Operations And Algebraic Thinking

#### Use the four operations with whole numbers to solve problems

These standards and example goals, would all be working on skills around actual computation. So if a student is struggling in computations, I would try to tie into one grade level of these standards.

#### A.1

Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

CCSS.MATH.CONTENT.4.OA.A.1

**Complex Example: **Student will be able to take a product in a single digit multiplication problem, and then use the multiplier and multiplicand to make statements about the product being so many times larger. Student will master this goal when they can verbally say the product is ___ times larger across 5 equations, with an average accuracy rate of 70%, across 10 trials.

**Complex Example**: Using a check list with steps to remember, Student will be able to interpret a single digit multiplication statement that a product is a specific times as many as the multiplier. Student will show mastery when they solve this across 3 statements, with an average accuracy rate of 80% across 10 trials.

**Simple Example:** Using a visual representation of a single digit multiplication equation, Student will be able to say the product is ___ times larger than ____, across 3 equations, with an average accuracy rate of 75% across 4 consecutive trials.

**Simple Example:** Student will be able to solve a multiplication problem with digits 1-5 and then say the multiplication sentence using correct vocabulary with on 3 multiplication problems, with 80% accuracy across 10 trials.

#### A.2

Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

CCSS.MATH.CONTENT.4.OA.A.2

*Note: see definition of multiplicative comparison here.*

**Complex Example:** Using a calculator, Student will be able to write a multiplication equation from a single digit multiplicative comparison, on 2 equations, with an average accuracy rate of 70% across 10 trials.

**Simple Example:** Given a multiplication chart, Student will be able to write a multiplication equation from single digit sentence using “twice as many” across 2 equations, and 10 total trials, with at least 80% accuracy. (consider doing a few other goals on three times, four times, etc.)

**Simple Example:** Given a multiplication problem from 1-10, Student will be able to draw a picture of two times as many, on 2 equations per trial, across 10 total trials with an average accuracy rate of 80%.

#### A.3

Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

CCSS.MATH.CONTENT.4.OA.A.3

*Note: This would be a great standard to create a goal and then benchmarks that include writing an equation with a missing quantity, check their work, or use estimation strategies.*

**Complex Example:** Using a graphic organizer, Student will be able to write an equation with a missing variable from a 4th grade level division or multiplication problem, with an average accuracy rate of 90% across 10 trials.

**Complex Example:** Student will be able to use estimation strategies to check their answer on two digit multiplication and division problems.

**Simple Example:** Using a graphic organizer, student will be able to solve 3 double digit multiplication word problems, with an average accuracy rate of 75% across 10 trials.

#### Gain familiarity with factors and multiples

#### B.4

Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.

CCSS.MATH.CONTENT.4.OA.B.4

**Complex Example:** Student will be able to use multiple addition or subtraction to find the factors of numbers 1-100, on 3 numbers at a time, across 10 trials with an average accuracy rate of 80%.

**Simple Example:** Given 5 numbers that are a multiple and factors, Student will be able to identify which number is a multiple and which numbers are factors. Student will master this goal when they can identify 3 sets of multiples, with 90% accuracy across 10 trials.

#### Generate and analyze patterns

#### C.5

Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.

CCSS.MATH.CONTENT.4.OA.C.5For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

**Complex Example:** Student will be able skip count by 5, 6, and 7’s with an average accuracy rate of 70% across 10 trials.

**Simple Example:** Student will be able to use a number line to count by 2’s across 10 trials with a 90% accuracy rate.

## Number & Operations in Base Ten

#### Generalize place value understanding for multi-digit whole numbers

These standards and example goals are all related to understanding numbers and counting. If a student is showing a weak understanding with “mathematical thinking” or “processes” these goals would be under those umbrella terms. (Also, when determining goals, you only need data to show that a student needs a goal. If you give them a test that shows these specific skills are a weakness, that is good enough.)

#### A.1

Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

CCSS.MATH.CONTENT.4.NBT.A.1For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

**Complex Example: **Student will be able to divide by multiples of 10 up to 1,000 on 5 sample problems per trial, across 10 trials, with an average accuracy rate of 70%.

**Complex Example:** Student will be able to multiply by multiples of 10 up to 1,000 on 3 sample problems per trials, across 10 trials, with an average accuracy rate of 90%.

**Simple(er) Example:** Student will be able to able to write the place value of 4 sample numbers (that could be between 1-1,000) in base ten numerals (450 is 400 + 50) across 10 trials with an average accuracy rate of 90%.

**Simple Example:** Student will be able to identify the place value of 5 numbers (from 1-100,000) with an average accuracy rate of 70% across 10 trials.

#### A.2

Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

CCSS.MATH.CONTENT.4.NBT.A.2

*Note: For this standard, and with most students, I would break it up into a few different goals. You could just benchmarks if you wanted to. You could put these examples together or use all of them.*

**Complex Example:** Student will be able to write the place value of 2 sample numbers (between 1-1,000,000) in base ten numerals and then determine which is larger or equal to each other across 20 trials with an average accuracy rate 90%.

**Simple(er) Example:** Student will be able to able to write the place value of 4 sample numbers (that could be between 1-1,000) in base ten numerals (450 is 400 + 50) across 10 trials with an average accuracy rate of 90%.

**Simple Example:** Student will be able to look at two numbers written as a base ten numeral (1-1,000), and determine if the number is greater, less, or equal, across 20 trials with an average accuracy rate of 90%.

**Simple Example:** Student will be able to compare two numbers (1-1,000) and determine if they are greater, less, or equal across 20 trials with an average accuracy rate of 80%.

#### A.3

Use place value understanding to round multi-digit whole numbers to any place.

CCSS.MATH.CONTENT.4.NBT.A.3

**Complex Example:** Student will be able to round 5, 4-digit numbers to the nearest thousand or hundred, across 10 trials with an average accuracy rate of 80%.

**Simple Example:** Student will be able to determine if 3, two digit numbers are closer to lower or upper multiple of ten (26 is closer to 30), across 20 trials with an average accuracy rate of 70%.

#### Use place value understanding and properties of operations to perform multi-digit arithmetic.

These standards go back to computing goals, but could also be used under mathematical concepts.

Fluently add and subtract multi-digit whole numbers using the standard algorithm.

CCSS.MATH.CONTENT.4.NBT.B.4

**Example:** Student will be able to add 3, 4 digit numbers (or less) with an average accuracy rate of 80% across 10 trials.

**Example:** Using graph paper to help organize numbers, Student will be able to add 2, 2 digit by 2 digit numbers with an average accuracy rate of 70% across 15 trials.

#### B.5

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

CCSS.MATH.CONTENT.4.NBT.B.5

**Example: **Using a multiplication chart, Student will be able to multiply 2, four digit by one digit, with an average accuracy rate of 80% across 10 trials.

**Example:** Student will be able to draw a picture to show 10, two digit multiplication problems, with 80% accuracy across 3 consecutive trials.

#### B.6

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

CCSS.MATH.CONTENT.4.NBT.B.6

**Example:** Student will be able to use a multiplication chart to help them divide four-digit dividends and one-digit divisors across 10 trials with an average accuracy rate of 90%.

**Example: **Student will be able to use a calculator to find the correct answer to a multi-digit division problem, with 100% across 3 consecutive trials.

## Numbers and Operations – Fractions

#### Extend understanding of fraction equivalence and ordering

#### A.1

Explain why a fraction

CCSS.MATH.CONTENT.4.NF.A.1a/bis equivalent to a fraction (n×a)/(n×b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

**Complex Example:** Student will be able to draw 3 picture of two equivalent fractions pairs, with an average accuracy rate of 80% across 10 trials.

**Complex Example:** Student will be able to use multiplication to find an equivalent fraction with 90% accuracy across 5 consecutive trials.

**Simple Example: **Student will be able to use a manipulative to show two equivalent fractions with 90% accuracy across 3 consecutive trials.

#### A.2

Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

CCSS.MATH.CONTENT.4.NF.A.2

**Complex Example:** Using a calculator, Student will be able to find a common denominator between two fractions, across 10 trials, with 5 fractions per trial, with an average accuracy rate of 90%.

**Complex Example:** Using a calculator, Student will be able to find a common denominator, then determine which fraction is greater or lesser, across 5 trials, with 2 fractions per trial, having an average accuracy rate of 70%.

**Simple Example:** Student will be able to compare two fractions with the same denominator across 5 trials with an average accuracy rate of 90%.

#### Build fractions from unit fractions

#### B.3

Understand a fraction

a/bwitha> 1 as a sum of fractions 1/b.CCSS.MATH.CONTENT.4.NF.B.3.A Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

CCSS.MATH.CONTENT.4.NF.B.3.B

Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.CCSS.MATH.CONTENT.4.NF.B.3.C

Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.CCSS.MATH.CONTENT.4.NF.B.3.D

CCSS.MATH.CONTENT.4.NF.B.3

Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

**Complex Example:** Student will be able to solve a fraction addition or subtraction word problem (with the same denominator), and create a picture of the two fractions, with 80% accuracy across 10 trials.

**Simple Example:** Student will be able to use fraction manipulatives to show how many equal pieces are in a fraction, with 100% accuracy across 3 consecutive trials.

#### B.4

Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

CCSS.MATH.CONTENT.4.NF.B.4

**Complex Example:** Student will be able to determine the operation being used in a word problem, and then multiply a fraction by a whole number, with 80% accuracy across 10 trials.

**Simple Example:** Student will be able to use manipulative to solve a multiplication problem of a fraction and whole number, with 70% accuracy across 15 trials.

#### C.5

Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.

CCSS.MATH.CONTENT.4.NF.C.5^{2}For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

**Example:** Student will be able to change a fraction with a denominator 10, to an equivalent fraction with denominator 100, across 10 trials with an average accuracy rate of 75%.

#### C.6

Use decimal notation for fractions with denominators 10 or 100.

CCSS.MATH.CONTENT.4.NF.C.6For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

**Example:** Student will be able to change a fraction with denominator 100 into a decimal with 80% across 20 trials.

#### C.7

Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

CCSS.MATH.CONTENT.4.NF.C.7

Example: Student will be able to compare two, two-digit decimals, across 5 questions, with 80% accuracy across 10 trials.

#### Measurement and Data

#### A.1

Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.

CCSS.MATH.CONTENT.4.MD.A.1For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), …

**Example:** Student will be able to multiply to find out the equivalent units in km, m, and cm. Student will mastery this when they can do this 5 times, across 5 trials, with 70% accuracy.

#### A.2

Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

CCSS.MATH.CONTENT.4.MD.A.2

**Complex Example: **Student will set up a fraction multiplication problem using distances across 10 trials with 70% accuracy.

#### A.3

Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

CCSS.MATH.CONTENT.4.MD.A.3For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

**Complex Example:** Student will be able to use fraction multiplication rules to solve a missing unit problem with 90% accuracy across 10 trials.

**Complex Example: **Student will be able to use a set up a fraction problem with a missing unit with 70% accuracy across 10 trials.

#### Represent and interpret data

#### B.4

Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.

CCSS.MATH.CONTENT.4.MD.B.4For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

**Example:** Student will be able to read a line plot and answer 3 literal questions about the data with 100% accuracy across 3 consecutive trials.

#### Geometric measurement: understand concepts of angle and measure angles AND Geometry

For these goals, I would only use them as needed. If a student is all caught up in other areas, it may be time to consider if they need a math goal. However, there is always an outlier case. Or if a student is in a classroom where they are never in the general education classroom, they may have a goal for this.