math problem solving goals 6th grade

Math IEP Goals For Special Education

Drafting IEP goals can be difficult, so here are a few math IEP goals (across various ability levels) to get you started. Please adapt and modify to meet the specific needs of your students. Keep in mind a goal should be a skill you believe is achievable by the student in 1 school year. You can always do an addendum if a student has met all criteria for the goal/objectives.

Remember, when writing objectives, break down the goal into smaller steps. You can lessen the percentage of accuracy, the number of trials (3/5 vs 4/5), or amount of prompting. Just make sure the objectives build on each other and are working towards mastery.

The reason why I always list accuracy at 100% when writing Math goals is because the answer is either right or wrong, an answer to a math problem can’t be 50% correct. So feel free to play with the ## of trials for accuracy.

Number Identification:

Goal: Student will independently identify numbers 1-20 (verbally, written, or pointing) with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: When verbally prompted by teacher to “point to the number _________”, Student will independently select the correct number with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: Student will independently count in rote order numbers 1-25 with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: Student will independently count by 2, 3, 5, 10 starting from 0-30 verbally or written, with 100% accuracy on 4 out of 5 trials measured quarterly.

One-to-one Correspondence:

Goal: When given up to 10 objects, Student will independently count and determine how many objects there are (verbally, written, or by pointing to a number) with 100% accuracy on 4 out of 5 trials measured quarterly/monthly.

Goal: When given up to 10 items/objects, Student will independently count and move the items to demonstrate 1:1 correspondence and identify how many there are with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: Given 10 addition problems, Student will independently add single digit numbers with regrouping with 100% accuracy on 4 out of 5 trials as measured quarterly.

Goal:  Student will independently add a single digit number to a double digit number with and without regrouping with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: Student will independently add double digit numbers to double digit numbers with (or without) regrouping with 100% accuracy on 4 out of 5 trials measured quarterly.

Adding with Number Line:

Goal: Given 10 addition problems and using a number line, Student will independently add single digit numbers with 100% accuracy on 4 out of 5 trials measured quarterly. 

Subtraction:

Goal: Student will independently subtract a single digit number form a double digit number with and without regrouping with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: Given 10 subtraction problems, Student will independently subtract double digit numbers from double digit numbers with and without regrouping with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: Student will independently subtract money/price amounts from one another with and without regrouping, while carrying the decimal point with 100% accuracy on 4 out of 5 trials as measured quarterly.

Goal: Using a number line, Student will independently subtract numbers (20 or less) with 100% accuracy on 4 out of 5 trials measured quarterly.

Telling Time:

Goal: Student will independently tell time to the half hour on an analog clock (verbally or written) with 100% accuracy on 4 out of 5 trials measured quarterly. 

Goal: Student will independently tell time to the hour on an analog clock (verbally or written) with 100% accuracy on 4 out of 5 trials measured quarterly.

Elapsed Time:

Goal: Given a problem with a start time and end time, Student will independently determine how much time has elapsed with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: Given a problem with a start time and duration of activity/event, Student will independently determine what the end time is with 100% accuracy on 4 out of 5 trials measured quarterly.

Dollar More:

Goal: Using the dollar more strategy, Student will independently identify the next dollar up when given a price amount with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: Student will independently identify the next dollar amount when given a price, determine how much is needed to make the purchase, and count out the necessary amount (using fake school money) with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: When given a price, student will identify which number is the dollar amount with 100% accuracy on 4 out of 5 trials measured quarterly.      

Money Identification/Counting Money:

Goal: When given a quarter, dime, nickel, and penny, Student will identify the coin and corresponding value with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: When given a random amount of coins (all of one type), Student will independently count the coins with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: When given a mix of coins (to include quarter, dime, nickel, penny), Student will independently count the coins with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: When given a mixture of coins and dollar bills, Student will independently count the money with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: When give 2, 3, and 4 digit numbers, Student will independently round to the nearest tens, hundreds, thousands independently with 100% accuracy on 4 out of 5 trials measured quarterly.

Greater than/Less than:

Goal: Given 2 numbers, pictures, or groups of items, Student will independently determine which number is greater than/less than/equal by selecting or drawing the appropriate symbol (<,>, =) with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: Student will independently count objects or pictures of objects and tally the corresponding amount (up to 15) with 100% accuracy on 4 out of 5 trials as measured quarterly.

Goal: Given a number, up to 20, Student will independently tally the corresponding number with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: Given data and a bar graph template, Student will independently construct a bar graph to display the data and answer 3 questions about the data with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: Given a line, pie, or bar graph, Student will independently answer questions about each set of data with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: Given data and a blank graph template, Student will independently construct the graph to display the appropriate data with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: Student will independently identify the numerator and denominator in a fraction with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: When given a picture of a shape divided into parts, Student will independently color the correct sections in to represent the fraction given with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: Student will independently add fractions with like denominators with 100% accuracy on 4 out of 5 trials measured quarterly.

Word Problems:

Goal: Student will independently solve one step addition and subtraction word problems with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: Student will independently solve two step word problems (mixed addition and subtraction) with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: Student will independently solve one and two step multiplication world problems with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: Student will independently read a one or two step word problem, identify which operation is to be used, and solve it with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: Given a word problem, Student will independently determine which operation is to be used (+,-,x, /) with 100% accuracy on 4 out of 5 trials measured quarterly.

Even/Odd Numbers:

Goal: When given a number, student will independently identify if the number is odd or even (written or verbally), with 100% accuracy on 4 out of 5 trials measured quarterly.

Measurement:

Goal: Given varying lines and objects, Student will independently estimate the length of the object/picture, measure it using a ruler, and identify how long the object/picture is with 100% accuracy on 4 out of 5 trials measured quarterly.

Multiplication:

Goal: Student will independently solve 10 multiplication facts (2, 3, and 5 facts) with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: Student will independently solve 20 multiplication facts (facts up to 9) with 100% accuracy on 4 out of 5 trials measured quarterly.

Goal: Given a division problem (where the divisor is _____), Student will independently solve it with 100% accuracy on 4 out of 5 trials measured quarterly.

Feel free to use and edit as necessary. It’s up to you how often you want to measure the goals, but remind parents that even if the goal says 5/5 times quarterly, it doesn’t mean you’re only working on it those 5 times. That is just the number of times you’ll take official data. Just make sure it’s a reasonable ## so you have time to take all the data you need. Especially if you have multiple goals/objectives to take data for!

Happy drafting!

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Math Goals for IEPs

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IEP Goals For Math

Welcome to our blog post on IEP goals for math! Setting goals for your child’s education is an essential step in their academic journey if you’re a teacher or the parent of a student with an Individualized Education Plan (IEP).

Many students find math difficult, so helping your child thrive in school by setting specific, measurable, achievable, relevant, and time-bound (SMART) goals might be helpful. This post will explore  what constitutes a strong IEP objective for math  and offer some starter  examples to get you going . Let’s get started, so grab a coffee and settle in.

What are IEP Goals for Math?

IEP goals for math are  specific, targeted objectives developed for students with an I ndividualized Education Plan (IEP) .  These objectives are intended to assist students with disabilities in improving their arithmetic skills and succeeding in the classroom. Each student’s IEP for math  should be customized to meet their specific requirements  and based on their existing knowledge and capabilities.

They should be  SMART objectives , which are specific, measurable, achievable, relevant, and time-bound. IEP objectives for math could center on several things, like  enhancing fundamental math abilities, problem-solving skills, or deepening comprehension of more complex arithmetic ideas . Parents and educators can assist students with disabilities in overcoming obstacles and succeeding in arithmetic by  creating clear and attainable goals .

For example, a measurable goal for a student may be “To develop basic math skills, such as addition and subtraction, by the end of the school year.” This goal is  measurable  because it has a time limit (by the end of the school year) and a particular objective (improvement). It is  relevant  because it directly relates to the student’s needs and academic pursuits. According to Understood.org , it is feasible since it is reasonable for the student to progress in this area within the allotted time frame. It is also time-bound because it specifies a deadline for completing the task.

It is  feasible  since it is reasonable for the student to progress in this area within the allotted time frame. It is also  time-bound  because it specifies a deadline for completing the task.

Teachers and parents can support students with disabilities to make progress and succeed in the classroom by establishing specific and attainable math IEP goals, as recommended by Great Schools .

It’s critical to frequently evaluate the student’s progress toward their IEP goals and revise them as necessary to keep them demanding yet doable. Read about the Special Education Math Curriculum to learn more.

IEP Goals for Math Problem Solving

IEP goals for math problem-solving are created to assist children with disabilities in acquiring the knowledge and methods required to comprehend and address mathematical problems. These objectives must be precise, catered to each student’s requirements and skills , and based on the student’s present performance levels and long-term goals.

Here are a few  additional points to consider when developing IEP goals for math  problem-solving:

• Focus on the student’s specific needs:  A thorough evaluation of the student’s present math ability should serve as the foundation for developing IEP goals particular to the student’s unique needs and abilities. For example, students who have trouble comprehending word problems can set a goal to enhance their capacity to read and understand mathematical word problems.
• Make the goals measurable:  IEP goals should specify specific performance indicators so that the student’s development may be monitored and assessed. To “increase the student’s accuracy in solving math problems from 75% to 90% within a six-month timeframe,” as an example.
• Make the goals achievable:  Given the student’s abilities and resources, the IEP goals should be achievable and realistic. For the learner to succeed and develop confidence, creating both demanding and challenging but not impossible goals is crucial.
• Make the goals relevant:  The student’s long-term goals and aspirations should be connected to the IEP goals to be meaningful, pertinent to the student’s needs and interests, and significant.
• Set a timeline:  A completion schedule for IEP goals should be included so that the student and their support team know the anticipated timetable for progress.

Functional Math IEP Goals Examples

Functional math IEP goals  focus on helping a student with a disability develop the math skills they need to function independently in their daily life .

Some examples of operational math IEP goals might include:

• “Within a three-month period, the student will be able to identify and make correct change when given a purchase amount and payment up to $5.00.”
• Within six months, the learner will be able to precisely measure and pour ingredients to follow a recipe with 90% accuracy.
• The student can arrange and keep track of appointments and activities within nine months with 80% accuracy using a calendar and telling time.
• Within nine months, “the learner will be able to compare prices and calculate sales tax and savings when shopping, with 80% accuracy.”
• “The student will be able to calculate and track a budget for a 12-month period, covering income and expenses.”

It is important to note that functional math goals  should be specific, measurable, achievable, relevant, and time-bound (SMART) and tailored to the individual student’s needs and abilities .

Jennifer Hanson is a dedicated and seasoned writer specializing in the field of special education. With a passion for advocating for the rights and needs of children with diverse learning abilities, Jennifer uses her pen to educate, inspire, and empower both educators and parents alike.

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34 6th Grade Math Problems: Answers With Worked Examples

Dr Suzette Takei

6th grade math problems signal a pivotal switch from concrete to abstract thinking in the math classroom. Teachers must act as facilitators to encourage critical thinking and problem solving skills, not just on the memorization of formulas.

In this article, we’ve listed 59 6th grade math problems to help students understand underlying principles and application of mathematics in real-world contexts. You can find all the math problems included in this article in a printable format in a convenient download.

What are 6th grade math problems?

6th grade math problems are math problems that suitably challenge 6th grade students to engage in abstract thinking. 6th grade is a pivotal year as students must switch from concrete to abstract thinking. 

Students who have spent 5th grade and their early elementary years focusing on reasoning skills and utilizing math manipulatives to bring math alive tend to transition to fractions , graphing , and algebraic concepts such as pythagorean theorem practice problems more easily. Teaching students to identify patterns, draw pictures or models, and reason abstractly through problems teaches them to persevere and approach multi-step problems with ease. 

Success in tackling 6th grade math problems depends on the following:

• Conceptual understanding of key concepts from the 6th grade math curriculum
• Effective teaching and support
• Elimination of math anxiety
• Practice in applying math and math formulas to a range of word problems

Math Games for 6th Graders

6 printable games for 6th graders that can be played in pairs, teams or as a whole class as a fun way to build math skills.

6th grade math curriculum

There are five critical overarching math concepts in 6th grade:

• Ratios and Proportional relationships
• The Number System
• Expressions and Equations
• Statistics and Probability

While it is beneficial for students to learn traditional algorithms, it is even more crucial for them to develop flexible thinking, recognize patterns, and employ strategies to understand word problems and devise effective solutions. 

To enhance mathematical comprehension and build perseverance in tackling multi-step problems, students must practice applying their mathematical skills in real-life contexts.

6th grade math curriculum: Common Core

Traditional mathematics teaching strategies emphasize formula memorization and specific learning patterns for each topic. 

In contrast, Common Core aims to cultivate a deeper understanding by introducing broader foundational methods of thinking and strategies aligned with comprehensive learning approaches. When effectively integrated, Common Core math enhances critical thinking and fosters a deeper understanding of mathematical concepts, moving beyond the traditional focus on memorizing and applying formulas. The real-world application of mathematical concepts better prepares students for college and careers.

How to teach 6th grade math problems

Drawing on my experience as a classroom teacher and the 10+ years of experience of Third Space Learning as one to one tutoring providers, here are some teaching strategies and ideas to enhance teaching and learning in your 6th grade math classroom:

1. I do, we do, you do

The I do, we do, you do approach allows teachers to model key skills and gradually release students to more independent practice. It offers a structured approach that enhances comprehension and retention of information. I do, we do, you do focuses students’ attention on essential information and provides a scaffolded resource that supports students as they tackle more complex, multi-step real-world problems.

In each of the 6th grade math problems included in this article, we’ve included step by step worked examples to support your classroom teaching.

How can Third Space Learning help with math?

The I do, we do, you do method is central to the Third Space Learning math tutoring curriculum from K-8th grade. In Third Space Learning’s one to one online math tutoring sessions, tutors guide students through a problem using the interactive classroom. 

The ‘Follow Me’ stage is where tutors break down new skills and concepts into manageable steps, providing verbal explanations and worked examples. Students complete a question with their tutor’s support, called ‘Your turn’. The worked example remains on the same screen for students to refer to as they work with their tutor to complete the new example. When students are ready, Third Space Learning tutors will gradually remove scaffolding to guide students to more independent practice. This stage is ‘You do’. 

At every stage, scaffolding, support, and questioning allow tutors to fully personalize the learning experience to support all learners to progress.

2. Engage students in meaningful math talk

Math talk is crucial as it promotes deeper understanding, critical thinking, and collaboration among students. Effectively articulating mathematical ideas and reasoning enhances students’ ability to communicate complex concepts logically.

3. Collaborative problem-solving

Collaborative problem-solving boosts student confidence and motivation. It helps students to view themselves as capable mathematicians and reduces math anxiety. Math discourse supports academic growth and cultivates essential skills needed for future educational and career success.

For each math topic included in this article, there’s a project idea to promote this all-important collaboration.

34 6th grade math problems and solutions 

In this article, you’ll find math problems and solutions for the following domains:

• Ratios and proportional relationships
• The number system
• Expressions and equations
• Statistics and probability

Under each domain, you’ll see:

• Practice exercises, guided notes and an answer key.
• Application problems designed to enhance students’ confidence and perseverance in solving word problems. 
• Project idea designed to promote collaboration, suitable for use in-class, as homework projects or even as a math club activity.

Ratios and Proportional Relationships: 6th grade math problems

6th grade students work with: 

• Mixed numbers
• Rational numbers
• Complete operations with fractions

Solving these ratio word problems involves using greatest common factors (GCF), least common multiples (LCM), solving proportional relationships and common denominators. 

Determine if each pair of ratios forms a proportion:

a) \frac{4}{2} and \frac{30}{6}

b) \frac{3}{2} and \frac{18}{6}

c) \frac{4}{3} and \frac{20}{15}

d) \frac{6}{18} and \frac{1}{3}

Answer : a) no, b) no, c) yes, d) yes

Solve each proportion:

a) \frac{x}{2} = \frac{30}{6}

b) \frac{15}{45} = \frac{2}{x}

c) \frac{12}{5} and \frac{x}{10}

d) \frac{7}{8} and \frac{56}{x}

Answer: a) x = 10, b) x = 6, d) x = 24, x = 64

A recipe requires 2 cups of flour for every 3 cups of sugar. If you want to make a double batch of the recipe, how much flour do you need?

Answer: \frac{2 c flour}{3 c sugar} x \frac{2}{2} = \frac{4 c flour}{6 c sugar}

4 cups of flour

A restaurant orders cans of black beans and cans of pinto beans. The ratio of the number of black beans to pinto beans is 2:3. What is the ratio of pinto beans to all beans?

Answer: Given: 2 black +  3 pinto = 5 total

2:3 = \frac{2 black}{3 pinto} and \frac{3 pinto}{5 all} = 3:5

Samir bought gas for his car.

• Gas cost $3.45 per gallon.
• Samir bought 11.5 gallons.

What was the total cost for Samir’s gas?

\frac{3.45 dollars}{1 gallon} = \frac{X dollars}{11.5 gallons}

\frac{3.45}{1 gallon} x \frac{11.5}{11.5} = \frac{39.675 dollars}{11.5 gallons}

He spent $39.68 on 11.5 gallons of gas

Ed and Jim are debating the answer to the equation \frac{2}{3}m = \frac{1}{4}m . 

• Jim states that m is equal to 2\frac{2}{3} .
• Ed states that m is equal to \frac{3}{8} .

Which statement is true?

a) Jim’s answer of 2\frac{2}{3} is correct because he divided \frac{2}{3} by \frac{1}{4} to get his answer.

b) Jim’s answer of 2\frac{2}{3} is correct because he divided \frac{1}{4} by \frac{2}{3} to get his answer.

c) Ed’s answer of \frac{3}{8} is correct because he multiplied \frac{1}{4} by \frac{2}{3} to get his answer.

d) Ed’s answer of \frac{3}{8} is correct because he divided \frac{1}{4} by \frac{2}{3} to get his answer.

 \frac{\ \frac{2}{3}m\ }{\frac{2}{3}} =  \frac{\ \frac{1}{4}\ }{\frac{2}{3}}

m = \frac{1}{4} × \frac{2}{3}

m = \frac{3}{8}

There are 4 cats for every 5 dogs in the pet store. How many cats and dogs could be in the pet store?

a) 64 cats and 80 dogs

b) 72 cats and 73 dog

c) 84 cats and 100 dogs

d) 96 cats and 110 dogs

\frac{4}{5} x \frac{2}{2} = \frac{8}{10} x \frac{2}{2} = \frac{16}{20} x \frac{2}{2} = \frac{32}{40} x \frac{2}{2} = \frac{64}{80}

 a) (-2) + (-8)     

b) (-3) – 7 + (-11)        

c) -1000 ÷ 10³      

Answer:        

a) – 2 – 8 = – 10

b) -3 – 7 – 11 = – 21

c) – 1000 ÷ 1000 = – 1

Add an inequality sign to show which number is greater.   a) (-6) ___ (-7)      

b)  -8 ___ 9         

c)  67 ___ 84

d)  -72 ___  -8  

e)  3 ___ -14

Answer: a) > , b)  <  , c)  < , d) < , e) >  

Question 10

What is the value of M on the number line?

 Answer: c) 7.5

Reasoning: Students need to estimate the value of each dash to determine the number represented on the number line. The number must fall between 5 and 10 which eliminates choice a and b; but 9, choice d, would be situated much closer to 10. The correct answer is c, 7.5.

Question 11

Which of the following numbers is greater than all the numbers in the list below? -3.25, – \frac{7}{2} -3.1, -3 \frac{3}{8}

b) – \frac{7}{2}

d) -3 \frac{3}{8}

Answer: c) – 3.1

Reasoning: Understanding that negative numbers are greater when they are smaller due to them being closer to 0. Thus, -3.25 can be eliminated immediately because -3.1 is greater. Converting – \frac{7}{2} = -3.5 so it can be eliminated as it is less than -3.1. Last, compare -3 \frac{3}{8} as a decimal is -3.333 which is also less than -3.1. Therefore, c, -3.1 is the correct answer.

Question 12

Which point shows the location of 43 on the number line?

Answer: b) Point N

Reasoning: Looking at the number line, students should recognize that each full point is broken into three sections. Thus, the individual lines can be counted as: 0, \frac{1}{3} , \frac{2}{3} , \frac{3}{3} = 1 , \frac{4}{3} , \frac{5}{3} … Therefore, R is \frac{4}{3} .

Question 13

Which list of numbers is ordered from greatest to least?

a) 1.5, \frac{2}{3} , – \frac{3}{4} , – 1.2

b) 1.5, -1.2, \frac{2}{3} , – \frac{3}{4}

c) \frac{2}{3} , 1.5, -1.2, – \frac{3}{4}

d) \frac{2}{3} , 1.5, – \frac{3}{4} , -1.2

Answer: a) 1.5, \frac{2}{3} , – \frac{3}{4} , – 1.2

Reasoning: Logically, negative numbers are smaller than positive numbers, thus, option b can be eliminated immediately. Understanding that when the numerator is smaller than the denominator you have a decimal less than one whole, students can eliminate option c and d as \frac{2}{3} < 1.5. The correct answer is a.

Question 14 

Sarah was hiking in the mountains. She started her hike at an elevation of 800 meters above sea level. She climbed up 250 meters to reach a peak and then descended 450 meters to a valley. What is her elevation at the valley?

Answer: 800 + 250 – 450 = 600

               Sarah is 600 meters above sea level.

Expressions and equations: 6th grade math problems

6th grade students must utilize their skills in working with order of operations and rational numbers to write equations from word problems and solve one-step and two-step equations. The solving of word problems involves working with fractions, divisors, integers, and percents in multi-step situations to determine the final value.

Question 15  

Evaluate the expression:

a) (5² -10) ÷ 5 x 2³

b) -3 x = 48

c)  \frac{1}{3}x = 9\frac{1}{3}

= (25-10) ÷ 5 x 8

= (15) ÷ 5 x 8

\frac{-3x}{-3} = \frac{48}{-3}

x = – 16

\frac{1}{3}x = 9\frac{1}{3}

\frac{1}{3}x = \frac{28}{3}

 \frac{\ \frac{1}{3}x\ }{\frac{1}{3}} =  \frac{\ \frac{28}{3}\ }{\frac{1}{3}}

x = \frac{28}{3} × \frac{3}{1}

Question 16

Sebastian pays $250 each month to rent an office where she earns $35 per hour tutoring students. Which equation represents Sebastian’s profit, y , for working x hours?

a) y = 35 + 250 x

b) y = 35 x + 250

c) y = 35 – 300 x

d) y = 35 x -300

Answer:  d) y = 35 x – 300

Reasoning: The starting amount he must pay is $250. The “per hour” implies multiplication as “per” means “to multiply.” Thus, the x must be multiplied by 35. Lastly, understanding that profit is determined by subtracting away expenses from any income forces the elimination of choices a and b. The correct answer is d, y = 35 x -300.

Question 17

Kedar runs the same number of miles, x , every week. His total distance run over the week is less than 60 miles. Which inequality represents how many miles Kedar runs each week?

Answer: d) x ≺ 60

Reasoning: The original problem states “less than 60” so students should recognize the need to plug in a number for the variable x to ensure the possible answer makes logical sense. Use 50, which is less than 60, and you can eliminate choice a and b. The determining factor is the number 60. Is “60 less than 60” or is “60 less than or equal to 60”. The problem wanted “less than,” thus, the correct answer is d.

Question 18

What is the value of (5 p + \frac{1}{4} )²  when p = 0?

Answer: (5 p + \frac{1}{4} )²

(5(0) + \frac{1}{4} )²

(\frac{1}{4} )²

Question 19

During a weekend special event, the manager of a bookstore gave away gift cards to every 75th person who visited the mall.

• On Saturday, 2,100 people visited the mall.
• On Sunday, 1,675 people visited the mall.

How many people received gift cards?

Answer: The manager gave away 50 gift cards.

Reasoning: To determine how many gift cards are given away, the student must recognize that the problem involves the need to divide the total number of people into groups of 75. 

\frac{total people}{75} = number of gift cards given away

\frac{3775}{75} = 50.33

The manager gave away 50 gift cards.

Question 20 

Maria is saving money to buy a new bicycle. She has already saved $45. Each week, she earns $15 from her allowance and an additional $10 from doing extra chores. She plans to save all of this money every week. How many weeks will it take for Maria to have at least $300 saved.

Step 1: Calculate how much Maria saves each week.15+10=25 dollars per week

Step 2: Set up an expression for the total amount saved after w weeks:

Step 3: Determine the number of weeks required for Maria to have at least $300 saved:

45 + 25 w ≥ 300

Step 4: Solve inequality:

-45               -45

\frac{25w}{25} ≥ \frac{255}{25}

Since Maria can’t save for a fraction of a week, she will need to save for at least 11 weeks to have at least $300.

Geometry: 6th grade math problems

6th grade geometry deals with using formulas, two-dimensional, and three-dimensional shapes, including parallelograms and quadrilaterals. Students must pay attention to customary units (metric, imperial, etc.) and use substitution and solving equations in addition to memorizing formulas.

Question 21

What is the area of the triangle rounded to the nearest hundredth?

Answer: 

A = \frac{1}{2}bh

A = \frac{3.5 × 3.5}{2}

A = \frac{12.25}{2}bh

A = 6.13 in²

Question 22

The graph shows segment AB and Point C

• Point M is located in the fourth quadrant.
• The distance between point C and point M is half the distance between point A and point B.
• Segment CM is parallel to segment AB.

What is the ordered pair of point M?

Answer: d) (2, -3)

Reasoning: Quadrant four is the lower right-hand quadrant without any existing points. Thus, the student would count line segment AB and determine the length is 10 units. Since half of 10 is 5, the student would count 5 units down from point C to point (2, -3)

Question 23 

Suzy is wrapping a cube-shaped box and wants to make sure she has enough wrapping paper. The net for the box is shown.

What is the area she needs to cover?

a) 73.5 cm²

d) 96.25 cm²

Answer: a) 3.5cm x 3.5cm x 6 = 73.5cm²

Reasoning: Students need to remember that surface area can be solved by adding the area of each shape. Since this is a cube, there are six identical sides. Area of a square is solved by multiplying length times width. Then, multiply that area times 6.

Question 24 

How much water can Sier hold in his fish tank if it has a length of 4 feet, a width of 3 feet, and a height of 5 feet?

Answer: V = 60 feet³

Reasoning: Students should recognize this as a rectangular prism and now that volume is the term related to how much something can hold. Therefore, the correct answer is:

V = L × W × H =

V = 4 feet × 3 feet × 5 feet

V = 60 feet³

Question 25

Calculate the length of the hypotenuse of a right triangle with legs measuring 6 cm and 8 cm.

Answer: 10 cm

Reasoning: Students will remember that the hypotenuse is the side opposite of the right angle and c  in the pythagorean theorem. Thus, 6 and 8 are the sides that form the right angle and used for variables a and b . Then, students will use the pythagorean theorem to solve for the hypotenuse.

(6)² + (8)² = c²

36 + 64 = c²

\sqrt{100} = c²

Question 26

Emma and John are playing a treasure hunt game on a coordinate plane. Emma’s starting point is at (2,3) and John’s starting point is at (8, -2). They both move to the treasure located at (8,7).

a) Calculate the distance Emma travels to reach the treasure.

b) Calculate the distance John travels to reach the treasure.

c) Determine who travels the longer distance.

Answer: a) Calculate Emma’s distance using the pythagorean theorem by first creating a right triangle where the 90° angle would be at (8,3); therefore 6 units right and four units up to the treasure.

(6)²+(4)² = c²

36 + 16 = c²

b) Calculate John’s distance to the treasure. Because it is a straight line, students can determine he is 9 units from the treasure.

c) John will travel further.

Statistics and probability: 6th grade math problems

Question 27

If the probability of picking a red marble from a bag is \frac{1}{4} ​, what is the probability of not picking a red marble?

a) \frac{1}{2} ​

b) \frac{1}{4} ​

c) \frac{3}{4} ​

d) \frac{1}{3} ​

Answer: c) \frac{3}{4} ​

Reasoning: The odds of an event occurring and the odds of the event not occurring must add up to 100% or 1 whole. Thus, if picking a red marble is \frac{1}{4} ​, then you subtract \frac{1}{4} ​ from 1 to determine the probability of the event not occurring.

not occuring + occurring = 1

x + \frac{1}{4} ​ = 1

– \frac{1}{4} ​       – \frac{1}{4} ​

x = \frac{4}{4} – \frac{1}{4}

x = \frac{3}{4}

Question 28 The following data set represents the number of books read by students in a class over a one month period of time: 3, 5, 8, 3, 6, 7, 3, 9, 5, 4.

a) Find the range.

b) Find the mean.

c) Find the median.

d) Find the mode.

a) Mean = 5.3

Reasoning: Mean is the average of the numbers. Add them all and divide by 10 because there are 10 numbers in the set.

\frac{3 + 5 + 8 + 3 + 6 + 7 + 3 + 9 + 5 + 4}{10} = \frac{53}{10} = 5.3

b) Median = 5

Reasoning: Ordered data = 3, 3, 3, 4, 5, 5, 6, 7, 8, 9. 

The middle two numbers are 5 and 5. Thus, take the average: \frac{5 + 5}{2} = \frac{10}{2} = 5

c) Mode = 3

Reasoning: This is the number that repeats most often.

d) Range = 6

Reasoning: Subtract the lowest number from the highest to determine range: 9 – 3 = 6

Question 29

The table below shows the number of hours students spend on homework per week:

a) What is the total number of students surveyed?

b) What is the most common range of hours spent on homework?

a) Total number of students: 4 + 6 + 8 + 2 = 20

b) Most common range (mode): 6 – 8 hours

Question 30

A jar contains 10 red, 15 blue, and 5 green marbles. If one marble is selected at random:

a) What is the probability of selecting a blue marble?

b) What is the probability of selecting a red or green marble?

a) Probability of selecting a blue marble = \frac{blue}{total   no.   marbles} = \frac{15}{10+15+5} = \frac{15}{30} = \frac{1}{2}

b) Probability of selecting a red or green marble = \frac{red + green}{total   no.   marbles} = \frac{15}{30} = \frac{1}{2}

Question 31

The following numbers represent the scores of 10 students on a math test: 45, 67, 72, 78, 81, 85, 88, 90, 92, 95.

Fill in the box and whisker plot labeling the median, lower quartile (Q1), upper quartile (Q3), the minimum and maximum numbers and enter their values.

Reasoning:  

Step 1: Order the numbers from low to high. 45, 67, 72, 78, 81, 85, 88, 90, 92, 95

Step 2: Determine the location of the following words: minimum, lower quartile, median, upper quartile, maximum. 

Step 3: Determine the minimum and maximum values and place in the first and last blue box. 

Step 4: Solve for the median by determining the number in the middle = 83

Step 5: Solve for the median of the lower half of the data set (lower quartile) by listing the first half of the numbers from low to high: 45, 67, 72, 78, 81. The median is 72 (the number in the middle).

Step 6: Solve for the median of the upper half of the data set (upper quartile) by listing the second half of the numbers from low to high: 85, 88, 90, 92, 95. The median is 90 (the number in the middle).

Question 32

Rosa is going to survey her classmates to find out if more students walk to school or ride the bus to school. Which sample method is biased?

a) Surveying 25 students chosen randomly on the bus

b) Surveying 25 students chosen randomly in the library

c) Surveying 25 students chosen randomly in the cafeteria

d) Surveying 25 students chosen randomly at an assembly

Answer: a) Surveying 25 students chosen randomly on the bus

Reasoning: Bias should be avoided in statistical analysis and surveys. Participants should be selected randomly, but from a location not involved in your survey.

Question 33

Which of the following describes independent events?

a) Choose a set of earrings, put them on, then choose another set of earrings. 

b) Draw a marble from a bag. Do not replace it. Draw another marble. 

c) Pick a vegetable for a side dish, then pick a meat for a main course. 

d) Pick a name from a hat. Do not replace it. Pick another name. 

Answer: c) Pick a vegetable for a side dish, then pick a meat for a main course. 

Reasoning: Independent events are events that do not depend on any other event. Solutions a, b, and d all alter the probability because the number of items to choose from is decreased when the first item picked is not returned to the set. However, option c, the number of vegetables is unlimited as is the type of meat. The meat and vegetables do not depend on each other or alter the number of choices.

6th grade math worksheets

Looking for more math worksheets and resources? See our 6th grade math test and selection of sixth grade math worksheets covering key 6th grade topics and more:

• Distributing Exponents Worksheet
• Dividing Decimals Worksheet
• One step equations Worksheet
• Ratio Problem Solving Worksheet
• Fraction to Decimal Worksheet
• Adding and Subtracting Integers Worksheet
• Exponential Notation Worksheet
• 9 Algebra Questions for Middle School
• Greatest Common Factor Worksheet
• Least Common Multiple Worksheet

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Math Games for 6th Graders [FREE]

On the lookout to make your math lessons fun and interactive while building math skills? Try our 6 printable math games for 6th graders.

Playable in pairs, teams or a whole class, our accompanying instructions and printable resources make preparation a breeze!

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Developing meaningful mathematics goals for ieps.

Published by

Rachel Lambert

In the last few months, several educators have asked me some variant of the following question:

How do we shift students’ IEP goals from rote memorization to meaningful mathematics?

IEP goals are the heart of instruction for students with disabilities. In my experience, a narrow goal can contribute to all sorts of unintended consequences for a child’s mathematics.  What kind of mathematics instruction might a child receive whose IEP goal states,

Given a set of numbers, STUDENT will solve two digit addition problems without regrouping with 80% accuracy in 4/5 trials.

In this case, it would then appear to be the civil right of the child to receive endless worksheets in addition without regrouping to prepare them to master this goal. Then when they mastered that sub-skill, they could be taught addition with regrouping in a separate set of worksheets. This kind of instruction will create mathematical habits in children that  we should not be encouraging: in this case, we are teaching the child that mathematics means applying memorized procedures when they are told to by the teacher, and does not include sense making or struggle. This creates children who, when you actually give them a meaty mathematical problem, ask you “but what is the operation?” We create that kind of learned helplessness in mathematics by oversimplifying and underchallenging children. So, in the endless cycle of educational unintended consequences, by following the child’s IEP, we provide instruction and assessment based towards a goal that will create a misunderstanding.  Whew.

IEP goals need to be specific, measurable, achievable, relevant and time-bound, and that structure contributes to overly prescriptive mathematical goals. When I first began work as a special educator, I saw some very non-specific IEP goals such as

STUDENT will learn multiplication.

I am not kidding.

So this movement towards more relevant IEP goals, goals that actually can be assessed, IS a civil right for a child with a disability. IEP goals are tools to ensure that a child with a disability is being educated, rather than ignored.  They should be taken seriously, and designed carefully for the good of that child.

But who will protect the children from overly-rote IEP math goals?

Here is a post called  Developing Mathematics IEP Goals and Objectives that Work! , that documents the work of a group of educators in Maryland who collaboratively redesigned IEP math goals to better align with standards-based mathematics,

The result of the collaboration was a tool that guides special educators through the development of student goals and objective that focus on a student’s long-term mathematics learning. The focus on learning behaviors is shifting our special educator’s thoughts about supporting mathematics instruction. Instead of mathematics views as a disconnected set of skills to be memorized, our teachers are viewing problems as puzzles with multiple solution paths and high levels of critical thinking. Additionally, our teachers are reporting that the scaffolding of the behaviors helps determine exactly where student skill levels lie and how to adjust instruction to advance their mathematical abilities. So, for the first time, IEP goals and objectives are aligned to the everyday instruction meaning that our students are pulled out of first instruction far less frequently. (

Because the mathematics goals were better aligned to the standards-based mathematics in the general education classrooms, this shift in IEP goals allowed students with disabilities to be pulled out of math class “far less frequently.”

Clearly, for us to rethink mathematics IEP goals, we need to design collaborations between general and special educators. In the case of these educators from Maryland, a team approach mattered. What also mattered was shifting the focus of IEP goals from computation to the Standards for Mathematical Practice. I might suggest that a learner could benefit from two mathematics IEP goals: one SMP goal, and one content goal.

Let’s think through an IEP goal based on the first Standard for Mathematical Practice:

MP1. Make sense of problems and persevere in solving them.

The first SMP is a critical goal for all kids, and particularly for any kid who either doesn’t fully invest themselves in mathematical work, or who tends to apply procedures without thinking through the problem. So how can we make this goal specific, measurable, achievable, relevant and time-bound?

As I write this goal, I think of a student I once had, let’s call him Joe. Joe was in a special education classroom with traditional mathematics instruction until 3rd grade, when he was placed in a general education classroom. Joe was a quiet, thoughtful child who found mathematics difficult, and would often sit with a math problem for long periods of time without starting. Because Joe had lots of practice in math following teacher procedures, and very little practice solving independently, he needed additional support to be able to begin and solve those problems. What about this goal for his IEP, inspired by SMP1, but with different wording?

When given a CGI story problem, Joe will use strategies such as representing the problem with drawings or manipulatives, reaching a solution in 4 out of 5 classroom sessions, documented by teacher observation and/or student work.

To assess IEP goals, special educators make sure it is SMART (Specific, Measurable, Achievable, Relevant and Time-bound). Is this goal specific enough that we could assess it? It specifies the kind of problem that we will assess, not just any math work, but CGI story problems. We would be looking for BOTH Joe using strategies such as drawing, but also him reaching a solution (no mention of whether it was correct or not).  We should be able to see him using these strategies, or direct-modeling the problem, as we observe him in class, and in his student work.  It is only slightly time-bound, that he must reach a solution during a classroom session. Adding additional time pressure, I believe, would be highly counter-productive.   Most importantly, it is relevant. If Joe was able to develop this new habit of making sense of mathematics, he would be able to tackle increasingly more challenging work.

The Standards for Mathematical Practices are made to be general, to cover many situations.  Using them as IEP goals means that they need to be made specific to the curriculum of the child’s classroom and the child’s particular needs.

A good IEP goal is also tied to instructional strategies. In this goal, a teacher would need to conference with Joe, coaching him strategically. How can we begin to solve a problem? We can visualize the problem, we can represent it in a drawing, and we can represent the problem using manipulatives. The first objective might be:

When given a CGI story problem and a teacher prompt , Joe will use strategies such as representing the problem with drawings or manipulatives,  reaching a solution 4 out of 5 classroom sessions, documented by teacher observation and/or student work.

Goals for other students using SMP 1 might look very different, depending on the child and the curriculum.

What can a group of educators work on to delve deeper into the mathematical IEP goals of their students?  First, you could begin by picking focus students, writing MPS IEP goals for them, and then carefully assessing their progress. To get started, you could analyze the mathematical goals in a goal bank (here is one developed in Oregon and appears to be in use in NYC). What is the cognitive demand of these goals? Which are tied to the MPS? How will you assess the student’s developing of reasoning? Of mathematical critique? You could track their participation in small group and whole group discussion.

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3 responses to “developing meaningful mathematics goals for ieps”.

Thanks for tackling such an important issue Rachel! You’ve left us lots to think about here but you’ve also provided some great suggestions. I really like the way that you’ve called for the teacher and student to conference with one another. We can learn so much about a student from just sitting down and listening to them.

Rachel, I love that I stumbled across this blog post of yours. Our team has been tackling the issue of how to write IEP goals that allow students to participate in an inclusive setting, and that align better with our school’s beliefs about learning. Thank you for this post! I’ve shared it with my team.

Hi, This is exactly what I’ve been attempting to do. The link to Oregon’s goalbank is not operational. Do you know where it moved to?

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How to Write SMART IEP Goals

A major task for special education teachers is writing Individualized Education Programs, or IEPs.  A major part of the IEP is the statement of annual IEP goals and objectives. 

We can think of the goal as being the destination that you want your special education student to get to by the end of a year. The services that you put into place support the goals that have been set a student with a disability.

Creating a quality goal with scaffolded objectives can take a lot of time and effort. So I want to show you one way in which you can break down this process into a series of manageable steps.  

Start with IEP Law

Before we dive into how exactly to go about writing goals and objectives, first let’s look at how IEP goals are defined by the Individuals with Disabilities Education Act:

(II) a statement of measurable annual goals, including academic and functional goals, designed to–

(aa) meet the child’s needs that result from the child’s disability to enable the child to be involved in and make progress in the general education curriculum; and

(bb) meet each of the child’s other educational needs that result from the child’s disability

Examine Content Standards

When creating academic goals for students with disabilities, it is important to ground the goals in the grade level content standards. This provides students with access to grade level curriculum as stated above.  

For many districts who are working with the Common Core State Standards, it is important to base grade level goals on how students are functioning within relation to these grade level content standards. 

Now let’s go through the process of writing SMART IEP goals:

Step 1. Identify the Standards that Meet the Student’s Needs

The first step in this process involves identifying the standard(s) that should be addressed.  You can start by identifying the grade level standards for the student. Standards have already broken out by grade level and have been organized by domain within this document.

By reviewing the student’s Present Levels, you can determine which standards the student may have the most difficulty with. Additional data sources should be used to select standards for student goals.

Teachers should then prioritize the standards based on those that would have the greatest impact on the student’s progress towards grade level.   For math, one consideration could be around the mathematics content at the student’s current grade level.

Major content in mathematics is considered the major work for the grade level. These are the areas in which general and special education teachers will need to spend most of their time throughout the year.  

Special educators can choose to focus on these areas when creating IEP goals. These are areas that will come up a lot during day-to-day instruction. To learn more about major content in math visit Achieve the Core for information. 

Step 2. Set Performance Target

The next step would be to set the performance target. You can utilized the Present Levels of Academic Achievement and Functional Performance in order to determine the baseline performance, historical rate of growth/progress, accommodations, and necessary supports needed to make the grade level content accessible for the student.

By deconstructing the standard and determining which components will promote student success, an individualized performance target can then be set.  

For example, in math, you may want to see a student demonstrate success through completion of a teacher generated worksheet with 80% accuracy over the course of 4 to 5 trials.

Step 3. Develop a SMART IEP Goal.

Special education teachers should ensure that they are keeping in mind what the acronym SMART stands for when developing goals:

S – Specific: The goal is focused by content (i.e. the standards) and the learner’s individual needs.

M – Measurable: Performance target is clearly stated and an appropriate measure is selected to assess the goal.

A – Attainable: Based on the student profile, it is determined that they have the ability to meet the performance target.

R – Relevant: Relevant to the individual student’s needs.

T – Time-bound: The goal is achievable within the time frame of the IEP.

Step 4. Develop SMART Objectives aligned to the selected IEP Goal.

There are three ways in which you can develop scaffolded objectives:

• Sequential benchmarks that demonstrate increasing fluency, independence, or accuracy
• Components of the goal
• Prerequisite skills

I prefer to develop objectives utilizing specific skills or components of the grade level, standards-based goal.  I find that by breaking down the content into workable chunks, I can develop lessons over a period of time that builds up to a grade level standard.  

When reviewing general education curriculum, one can see that teachers are rarely tasked with tackling an entire standard within one lesson. To expect a special education student to tackle an entire standard in one goal or objective is also pretty unrealistic.   

At times, it may be necessary to create scaffolded objectives to provide students with prerequisite skills from the current or previous grade levels.  The data may indicate that many of your students need the standards deconstructed in this way. This helps the student meet the grade level goal that was developed.

When following the steps listed above, I created the following IEP goal for a third grade student:

By____ when given a teacher generated problem set, manipulatives, and a prompt, Student will interpret whole number quotients of whole numbers by drawing a picture and describing a context that indicates the partitioning of a total number objects into equal shares as measured by 80% accuracy on at least 4 out of 5 trials.

When really unpacking the standard and digging into the content, I decided that I would create four scaffolded objectives that would support the student in meeting their grade level goal:

By____, when given a teacher generated problem set and a prompt, Student will interpret whole-number quotients as the number of objects in each group when partitioned into equal groups by drawing a picture and providing an explanation with 80% accuracy on at least 4 out of 5 trials.

By_____, when given a teacher generated problem set, manipulatives, and a prompt, Student will represent a situation with a division expression with 80% accuracy on at least 4 out of 5 trials.

By ____, when given a teacher generated problem set, manipulatives, and a prompt, Student will represent a division expression with a situation by drawing a picture and providing an explanation with 80% accuracy on at least 4 out of 5 trials.

When I really think about the deconstructed standard and review student weaknesses,  I may find that instead of breaking this standard out by the grade level content covered, I may need to include another goal that supports prerequisite skills that I will address prior to going into this standard. 

When considering the example above, we ask, “is the student ready for division even with the supports included in the goals and objectives? Would it make more sense to attack addition, subtraction, and multiplication first?”  

This is where the individualization comes into play and where you really have to be strategic in how you write the annual goal.   Every IEP goal should be specific to the individual, but it helps to have a process to follow to make creating these goals a bit easier.

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IEP Goals For Math Problem Solving

Last Updated on October 8, 2022 by Editorial Team

Math problems may prove exceptionally difficult for students with learning disorders. Thankfully, the schools are now adopting a sincere approach to making education quite inclusive for children with special education needs. In addition to offering individualized education programs , they insist on working with parents/guardians as a team. So, if you are a parent or caretaker of a child with math learning difficulties, you must know about IEP goals approved under the special education program.

In this post, we intend to acquaint you with IEP goals for math problem-solving. By having knowledge of these IEP goals in hand, teachers and parents can ascertain the effectiveness of the program. Also, they can evaluate the program implementation procedure and include changes in a student-centric manner when required.

Measurable IEP goals for math problem-solving

IEP is the right of students with learning difficulties. It has got the backing of IDEA (Individuals with Disabilities Education Act), which is a law.

The law dictates that schools arrange for suitable interventions to help children with special needs meet their educational goals. Governed by these laws, the following is a list of measurable math problem-solving IEP goals:

• The goal for building number sense: By the end of the x period, child A will subitize n number of sets containing 10 or few items with 80% accuracy. This goal is suitable for the K2 level and may be repeated till the attainment of perfection.
• Pattern identification: A major part of math problem-solving is dependent on the ability to sequence numbers or identify patterns. It is part of math reasoning and the goal reads as, “The student will identify and explain the pattern at least twice with a minimum of 70% accuracy at the end of the academic session.”
• Find fractional values: Moving from whole numbers, a student must be familiar with certain parts of it. Hence, the IEP goal for learning fractions includes “the student will identify half, one-third, and one-fourth of a quantity by the end of the chosen period with 70-80% accuracy.”
• Attain Operational fluency: By the end of Grade 3, the teacher may strive to impart fluency in doing mathematical operations on whole numbers up to1000 using manipulatives . A suitable format of goal will be, “The student will recall all operational facts, interpret products of whole numbers, and write a verbal expression of mathematical equations with almost 100% accuracy in ‘n’ number of attempts.”
• Learn geometry problem-solving: Corresponding to the expectations from students of Grade 5 and Grade 6, the student with individualized education needs shall demonstrate fluency in calculating the perimeter, area , and volume of a given set of geometrical figures (mostly, square, rectangle and circle).
• Polynomial expressions’ expansion, combination, and simplification mastery with 80% accuracy
• Tabulate and solve graphs based on equations and inequalities
• One-step and multi-step linear equations are to be solved using correct strategies 8/10 times with 80% accuracy
• Determine slope with at least 80% accuracy from given ordered pairs or equations or graphs

More or less, the IEP goals for math problem-solving surround these classic branches of the subject. With the increase in grades, the level of difficulty changes.

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having  just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of  Smartynote -‘The notepad app for dyslexia’, 

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Math IEP Goals for Fifth Grade Skills

Welcome to teachtastic's iep goal bank., back to the main page.

Add Decimal Numbers

Add Fractions

Add Fractions Using Models

Add Mixed Numbers

Add and Subtract Decimal Numbers

Add and Subtract Decimal Numbers in Word Problems

Add and Subtract Fractions in Word Problems

Add and Subtract Mixed Numbers in Word Problems

Add and Subtract Money

Add and Subtract Whole Numbers in Word Problems

Complete Addition and Subtraction Sentences for Fractions

Complete Mixed Number Addition and Subtraction Sentences

Describe Properties of Addition

Estimate Mixed Number Sums and Differences

Use Properties of Addition

Use Rounding to Estimate Decimal Sums and Differences