**The Student** was a twelve year old boy diagnosed as being developmentally delayed. He lives in the U.S., although his first language is not English. He was enrolled in an academic tutorial program to prepare him for school entry. His program includes language, reading (decoding), reading comprehension, math, spelling, cursive and creative writing. In the beginning, attention was focused on developing fluent language skills, basic decoding skills and counting skills as a starting point for arithmetic.

**The Tutor(s) **This student had two tutors. His first tutor was a beginning primary elementary school teacher just about to start her first job. She taught him through June, July and part of August. His second tutor was a homeschooling mother who had successfully homeschooled her four children. Both tutors were trained in the Maloney Method by me using Skype, email and fax. I never did to meet face to face with the tutors, the student or the parents involved.

**The Results **From the beginning of May and while being tutored for 12 hours per week during a period of a year, this student completed:

· All 450 lessons of the *Distar Language *programs

· All 50 lessons of the *Counting Skills* program.

· All 120 lessons of the *Toolbox Series for Literacy*.

· 130 lessons of the *Addition and Subtraction* modules of *Corrective Mathematics*

He then continued to be tutored in

· The *Multiplication* module of *Corrective Mathematics*

· The *Level A Corrective Reading Comprehension* program.

· The *Level 3 Teach Your Children to Read Well* program.

To move to the next fluency check, the student must correctly identify 25-30 sounds or sound combinations in 30 seconds while making 2 or fewer errors. The chart below provides the scores for each attempt and the total number of days for the student to complete the 60 lesson program with fluent performances on all sounds and sound combinations.

**The Measurement Targets **At the end of each lesson, the student does a series of timed measurements. Four of these measurements relate to his decoding skills, These fluency checks test the student’s fluency with:

- Sounds and sound combinations up to and including that lesson.
- Word lists of words taught to that point in the program.
- Story reading of a story constructed completely of words taught in the program to this point.
- Vocabulary meanings of words already learned.

**The Program **included:

- All three levels of the
*Direct Instruction Language*program created by Engelmann and Osborne. (450 lessons @ approximately 20 min./lesson) - Both levels of the
*ToolBox Series for Literacy*and the final 2 levels of*Teach Your Children To Read Well*series created by Maloney, Brearley & Preece. (240 lessons @ 30 min/lesson) *Counting Skills*created by Michael Maloney (50 lessons @ 15-20 min/day)- All 8 modules of the
*Corrective Mathematics*program created by Engelmann and Silbert (500 lessons @ 30 minutes /lesson) *Corrective Spelling through Morphographs*created by Engelmann and Dixon (140 lessons @ 30 min./lesson)- All 4 levels of the
*Corrective Reading (Comprehension) Series*created by Engelmann and (335 lessons @ 30 minutes /lesson) *Quickwrite*by Michael Maloney for creating a creative story draft in 8 minutes (daily lessons).

Most people pay scant attention to cursive writing skills, but this inability can be a major barrier to completing written tasks, especially for children in elementary classrooms. Students are forced to rely on their printing skills when cursive is not carefully taught. Generally in elementary schools today, there is little formal instruction as to how one creates letters or numbers, and even less supervised practice. As a result, many students have time-consuming cursive writing skills and write only when absolutely necessary. They do not do much better writing numerals.

There are a number of common errors such as students writing numerals from the bottom up instead of from the top down. These patterns are generally ignored with the result that the students remain slow numeral writers. Worksheets and homework take much longer than necessary and are demoralizing for many children. **How do your kids write numerals?**

The teaching of writing skills has numerous component skills which make up the composite behavior. Each of these component skills can be measured and taught if necessary.

**Forming Numbers**

** **Writing digits is less complicated than forming either printed symbols or cursive writing letters. When forming numbers there is a simple rule. All numbers start from the top and go downwards. Students begin by putting their pencil tip on the dot and then following the arrow in the correct direction.

2, 3, and 9 start at the dot and are directed by the arrow to go upwards to the right and then down.

0, 1, 6, and 8 start at the dot and are directed by the arrow to move downwards.

7 starts at the dot and goes across to the right and then down at an angle to the left.

5 starts at the ball and goes horizontally to the left, then down and to the right.

4 requires the student to make two separate motions, both starting from the top and going down. The first movement is exactly like writing a 1. The second stroke starts at the top then crosses the first stroke by moving horizontally to the right.

It is easy to see how a student could be confused about where to start and how to determine the direction and/or angle of the rest of the stroke in order to form any of these numerals.

To reduce this confusion we will separate the numerals into groups which require identical or similar strokes.

The initial group consists of 1 and 7

The second set is comprised of 2, 3, and 9

The third set is made up of 0, 1, 6, and 8

The final set has only the numeral 4 because it is the only one that requires two positioning of the pencil and two distinct movements.

**See/Trace Numerals**

Some students are capable of seeing an example and copying it. Others require more careful guidance as seen in tracing the numerals. Copies of the required practice sheets for tracing numerals are appended to this document.

** See/Write Numerals**

** **The student is provided with a model of the numeral. A dot indicates the starting point. An arrow designates the direction of the stroke. One or more numerals using the same types of strokes can be initiated at the same time. If the student cannot create 50-60 strokes per minute should be given the task of tracing the numerals first. Once they have achieved 50 – 60 strokes per minute tracing numerals, they can attempt the see/write numerals task.

When the student can create 50-60 numerals per minute for each of the four tasks, they can begin to write the entire set of numerals from 0-9.

Number writing from 0-9 is a second tool skill that indicates the speed and accuracy with which a student can produce readable numerals. This task is done for 30 seconds by having the Student and Student repeat the numbers on a sheet of lined paper as quickly and accurately as possible. Again Think/Say counting from 0-9 is generally a task with which the student is already fluent, so the speed of their pen or pencil will not be slowed by knowledge of the next number to be written. The model looks like this;

0 1 2 3 4 5 6 7 8 9 repeated as often as possible for 30 seconds.

In order to See/Write the answers to 50 single digit math facts, the students will need more than 125 numerals since many answers will demand two numerals. The fluency level is between 125 and 150 numerals per minute with no more than 2 errors. Once again, any numeral that cannot be deciphered on a hand-printed price tag is considered an error. The standard for fluency is 0-2 errors per minute.

]]>Yesterday I received a telephone call from a fellow educator. His dream is to build a digital conduit for teachers through which good ideas and good lesson plans could be shared. While I liked his excitement, I also noted my reservations, namely that well-designed lessons needed a certain quality.

· They have to cover a domain of knowledge.

· They must reveal the rules or phenomenon by which that domain operates.

· The lesson must teach both examples of when the phenomenon applies and non-examples of when it does not.

· Students need to be taught to fluent levels of performance

For example, in teaching students correct spelling, there is a rule which determines whether you pluralize nouns and verbs by adding either “s” or “es” to the end of the word.

· The rule covers the complete domain of English nouns and verbs.

· A well-designed lesson would present the students with examples (e.g. churches, taxes, brushes, etc.)

· and non-examples (e.g. robots, dogs, dinosaurs).

· The students would be taught the rule that if the word ends with “ch, sh, s, x, or z” use “es” to make it plural.

· If it does not end “ch, sh, s, x, or z” use “s” to make it plural.

· Students would be taught to apply the rule to examples and non-examples at the rate at which they can write without making more than 2 errors.

Lessons designed by teachers do not tend to meet these standards. There is a very good reason for that. Our teachers are rarely provided with this level of training in instructional design. They simply have not been given the tools – just the responsibility. Competent instructional designers are as scarce as hen’s teeth.

Secondly, well-designed lessons need to be field tested, their flaws discovered and repaired so that students come away from the lesson with one and only one interpretation of the phenomenon under consideration.

Interestingly enough, we have had this level of design within education for almost 50 years and have chosen to ignore it. The best designed curricula has been exhaustively studied in a national research study over a multi-year experiment which compared the effectiveness of various methods involving hundreds of thousands of students and costing more than a billion dollars.

A couple of years ago, the What Works Consortium, the agency of the U.S Federal Dept. of Education, that determines which research will be distributed, decided unilaterally to discontinue disseminating the results of Project Follow Through ( the source for the comparative research) and of the Sacajewea Study ( the research on the importance of measuring results) because they were more than 20 years old.

This decision occurred as both of these leading methods (Direct Instruction and Precision Teaching) were making a comeback in public education, especially for children with learning deficits.

If we decide to unilaterally suspend the empirical results of educational research, I propose that we have to cover all of the scientific domains and renounce all of the laws of science. Let’s start with the Law of Gravity. It is much more ancient than Direct Instruction and it sucks.

Oh, by the way, if you need the other 13 spelling rules, contact me. They are old, but they work wonderfully.

]]>On April 1, 2019, the University of West Florida hosts the official launch of the fourth series of the Maloney Method Integrated teaching strategies course. Three major behavioral methods combine to assist individuals with language and literacy deficits, including those on the ASD spectrum.

The 12-week long course is the largest amalgamation of Behavior Analysis, Direct Instruction, Precision Teaching and Fluency Building Practices. This teaching method started in 1975 with Michael Maloney and Eric and Elizabeth Haughton in Belleville Ontario, Canada.

In 1979, Maloney established the original, for-profit, behaviorally-based learning center and school in North America. His local school district rejected the methods and dismissed him and Eric Haughton, despite their consistent successes with at-risk students.

The course provides 12 CEU credits and extends over 12 weeks with 6 video presentations and 6 live labs. All materials are archived to provide maximum flexibility for the registrants, many of whom will likely be Board Certified Behavior Analysts working with children and youth on the autism spectrum.

The initial pilot project, which concluded in June of 2018, received consistently high reviews from the students involved.

The course registration is open to the first 50 registrants who sign up.

The course costs US$ 399.00.

Click here to go directly to the University of West Florida Course Description.

Call Michael at 1-877-368-1513 (EST zone). Leave a message, time zone and good time to return the call.

Behavioral interventions require data. Decisions are made on the basis of the data collected. Decisions for program changes take into account the performance of the client, often as a frequency count, sometimes within a given period of time. The data is charted so that it can be shared with other stakeholders in case conferences, research papers, staff meetings and professional conferences.

Many years ago while working in classrooms with special needs students, my colleague, Eric Haughton showed me a simple hands-free tool for collecting data – a bead counter made from a shoelace, a clip and some beads, which attached to my belt. See the picture below.

* Make sure you select a flat athletic lace that is twenty-four inches in length. (beads slide down on round laces).

* The lace is tied so that it has two different length strands.

* As well, knots are tied at different levels along each of the two strands.

* Each strand has a knot tied above the beads, nine beads and a second knot tied below the beads. The fifth bead in each strand is a different color.

* The longer strand of beads becomes the one’s column. The shorter strand becomes the ten’s column.

Move both sets of beads to the top knot of its strand to begin. Clip the counter to some part of your clothing. Each time you observe the targeted behavior, simply slide one bead in the one’s column down to the lower knot. When you move the last bead in the one’s column to the bottom knot, you have a score of nine. When the next targeted behavior is observed, you move all of the beads on the one’s column up the strand to the top knot. Then you move the bottommost bead in the ten’s column down to the lower knot on the ten’s strand. Now you have a score often. Repeat this process throughout the observation period. The bead counter can record up to 99 incidents of the targeted behavior. At the end of the observation period record your data on the chart.

How did you do? If you want to share your experiences, or share your data charts, write a comment, or call 1-877-368-1513. Looking forward to hearing from you!

]]>The Maloney Method has teamed up with the University of West Florida ABA department to offer this online course, now open to the public.

The course prepares participants to teach fundamental literacy skills to students (children or adults) on the autism spectrum and individuals at risk of school failure.

You learn how to use Behavior Analysis, Direct Instruction and Precision Teaching. The course uses material that addresses basic behavior skills, pre-language activities, reading lessons, and mathematics programs.

Click here to read the complete course description on the UWF website.

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**Behavior Objective **

The student can See/Mark 80-100 nouns in sentences with 2 or fewer errors/minute.

The worksheet has a number indicating how many nouns are in that sentence.

**Materials **

- Pencil
- Timing Device
- Student to practice this script with
- One Standard Celebration (SCC) Chart (print from course files)

**Discussion **

A noun tells of a person, place, thing or state of mind (e.g. confusion).

Students need to learn grammar skills in order to learn communication skills well. They also require grammar skills in order to analyze deductions so as to know how to write a correct conclusion.

One rule about deductions is that the noun which is found in the rule and the middle part cannot be used in the conclusion. If students cannot quickly and accurately identify nouns, they are much more likely to make errors in writing conclusions to deductions.

Teach your students to recognize nouns using the lesson provided before you begin to teach them reading comprehension skill, especially deductions. Present the first five examples as a lesson. Then let your students try the rest of the set independently. This lesson only deals with identifying nouns in one of the four possible kinds of deductions. While identifying nouns will be useful for all types of deductions, further lessons for other types of deductions are still required and will follow later.

**Teaching Regular Nouns **

**Script **

Say to the student, “**Now we are going to learn about parts of speech called nouns. I am going to teach you some rules so that you can tell which words in a sentence are nouns. Knowing about nouns is important when you are writing stories or notes.” **

Say, “**Here is the rule about nouns. My turn. Listen. A noun tells about a person, place or thing. Listen again. A noun tells about a person, place or thing. Say the rule with me about what a noun tells. Ready.” **

The student and the teacher say, “*A noun tells about a person place or thing.”
*Say to the student, “

**person, place or thing.” **

Say to the student, “**Now it is your turn to say the rule about what a noun tells. Ready.” **

The student answers, “*A noun tells about a person, place or thing. *

Say to the student, “**That’s correct.“ **

Practice until the student can say the rule correctly, quickly and easily.

Say to the student, “**Good learning that rule. You’ve got it. Now let’s use the rule to find the nouns in a sentence. Look at Part A of the worksheet below and read me the first sentence.” **

The student reads, “*Bits of fur floated in the air.”
*Say to the student, “

**nouns are in this sentence. What does that number say?” **

The students says “*Three”
*Say to the student, “

Say to the student, “**That’s correct. Let’s see if you can find the three nouns in the first sentence. Use your rule about nouns to find the first person, place or thing in that sentence. What is the first word that names a person, place or thing in that sentence?” **

The student says, “*Bits.*”

Say to the student, “**That’s right, the first noun names a thing “bits”, Good going.”
**

**Correction Procedure **

If the student makes an error, point to the word “bits” and say, “**My turn. Does the word ‘bits’ tell me about a person, place or thing? Yes, it tells me about a thing. A ‘bit’ is a thing. ‘Bits’ are things. Read the sentence again.” **

The student reads the sentence again.

Say to the student, “**Good reading. Now look at the sentence. What is first word in this sentence that names a **

**person, place or thing?” **

The student says, “*Bits.” *

Say to the student, “**That’s right. Now find the next noun in that sentence.” **

The student says, “*fur” *

Say to the student, “**Good using your rule. ‘Fur’ is a thing, so ‘fur’ is a noun. Now find the third noun in the sentence.” **

The student says “*air”. *

Say to the student, “**Right again. ‘Air’ is also a thing, so ‘air’ is a noun. Tell me all three nouns in that sentence.” **

The student says, “*Bits, fur and air” *

Repeat with several additional examples from **Part A **of the worksheet until the student is naming nouns quickly, easily and without error.

Then let the student complete Part A of the worksheet as you watch. Correct any errors immediately using the correction procedure given above.

**Teaching Proper Nouns **

**Script **

Say to the student, “**Now we are going to learn a second rule. This is a rule about a special kind of noun. This is a rule about proper nouns. Listen. A proper noun tells about special individuals, events or places. Proper nouns always begin with a capital letter. Listen again. A proper noun tells about special individuals, events or place and always begins with a capital letter. **

Say to the student, “**Say that rule with me. Ready.”
**The teacher and the student say the rule together, “

Practice until the student can say the rule correctly, quickly and easily.

Say to the student, “**Good learning that rule. Now say the rule all by yourself. Ready. **

The student says, “*A proper noun tells about special individuals, events or places and always begins with a capital letter.” *

Say to the student, “**You’ve got it. Now let’s use the rule to find the nouns in sentences. Look at Part B of your worksheet. The title says ‘proper nouns’. Read me the first sentence of Part B.” **

The student reads, “*General George Washington became the first president of the United States after the Revolutionary War.” *

Say to the student, “**Good reading. The number at the end of the sentence tells you how many nouns are in that sentence. How many nouns are in this sentence?”**

The student **says, **“*Four” *

Say to the student, “**That’s correct. The sentence has four nouns. Some of these nouns might be proper nouns. So what is the first noun in that sentence? Use your rules about nouns and proper nouns to figure it out.” **

The student says, “*General George Washington.”
*Say to the student, “

Say to the student, “

Say to the student, “ **Why is it a regular noun?” **

The student says*, “In this sentence, president does not name a special person.” *

Say to the student, “**That’s correct. What is the next noun?” **

The student says, “ *United States” *

Say to the student, “**Is United States a regular or proper noun?” **

The student says, “*United States is a proper noun because it names a special place.” *

Say to the student, “**Good using your rule. What is the last noun in that sentence?” **

The student says, “*Revolutionary War.” *

Say to the student, “**Is Revolutionary War a regular noun or a proper noun?” **

The student says, “*A proper noun because Revolutionary War names a special event.” *

Say to the student, “**Nice work. You are right again. Let’s do the next sentence.” **

Repeat the procedure with the next 10 sentences. Then give the student a chance to do the rest of the sentences independently as you watch. Correct all errors immediately.

**Measuring Progress – The One-Minute Timing **

Say to the student, “**Now we will do a one-minute timing of your knowledge of nouns. Look at Exercise C on your worksheet. You will read each sentence and underline each regular noun and circle each proper noun. What are you going to do with each regular noun?” **

The student says, “*Underline it.”
*Say to the student, “

Say to the student, “**That’s correct. I will give you one minute to underline or circle as many nouns as you can. You may start as soon as I say ‘Please begin’. You will stop after one minute when I say ‘Thank you’. Ready. Please begin.” **

Time the student for one minute, then say, “**Thank you.” **

Correct the student’s work. Correct any errors and review them with the student. Record the number of correctly marked nouns and the number of errors on the chart. Have the student complete the worksheet for additional practice. The student should be able to mark between 80 and 100 nouns in one minute with no more than 2 errors.

**Teaching Regular Nouns – See / Mark Nouns **

**Worksheet – Part A**

**
**Find the

**Bits of fur floated in the air. (3)****Seven spiders sat on a large leaf. (2)****Three dogs, two cats and a monkey went for a walk in the park. (5)****Are you going there right now? (0)****How many cookies did you eat? (1)****Get off the boat! (1)****When the rain started, all of the players left the field. (3)****The birds sat on the wire and made a lot of noise. (4)****Who has the green jacket and the green hat? (2)****The tall woman wants two pairs of shoes. (3)**

**Teaching Proper Nouns – See / Mark Nouns **

**Worksheet – Part B**

**
**Find the

1. General George Washington became the first president of the United States after the Revolutionary War. (4)

2. When the game was over the Bandits had scored two goals. (3)

3. The second runner tripped on Main Street. (2)

4. “Captain Brant wants to see you right now”, she said.

5. Mayor Thompson cancelled the parade.

6. The mayor cancelled the Fourth of July parade.

7. That mountain range has very high peaks.

8. The Rocky Mountains have very high peaks.

9. Which book would he like to read?

10. The Wizard of Ox is a great book for him to read.

11.Seven lizards ran into the pond.

12. Miguel, the producer of the movie, won a big award.

13. The director did not win any awards.

14. When was the last time you went to the dentist?

15. Who took it and where did they go?

16. During the Second World War, General Patton was well known.

17. At the Tour de France, all of the riders have to be very fast.

18. Man of War won the Kentucky Derby in record time.

19. The company will ship your order today.

20. The rain fell on London for ten more days.

21. How fast will that Honda go?

22. How fast does your car go?

23. Barnum & Bailey created a large circus with many animals.

24. The Washington Post has a large staff of writers.

25. Many of the authors did not come back after lunch.

26. John Steinbeck, the author of * Grapes of Wrath, *wrote many other books.

27. Queen Elizabeth has a very busy travel schedule.

28. The Titanic hit an iceberg and sank.

29 The World Series usually starts in October.

30. When the branch broke, the boy fell out of the tree.

**Teaching Proper Nouns – See / Mark Nouns **

**Teaching Regular and Proper Nouns **

**Worksheet Part C – Measuring Progress – The One-Minute Timing**

Read each sentence and underline each regular noun and circle each proper noun.

- General George Washington became the first president of the United States after the Revolutionary War. (4)
- When the game was over the Bandits had scored two goals. (3)
- The second runner tripped on Main Street. (2)
- Queen Elizabeth has a very busy travel schedule. (2)
- The Titanic hit an iceberg and sank. (2)
- The World Series usually starts in October. (2)
- When the branch broke, the boy fell out of the tree. (3)
- Bits of fur floated in the air. (3)
- Seven spiders sat on a large leaf. (2)
- Three dogs, two cats and a monkey went for a walk in the park. (5) Are you going there right now? (0)
- How many cookies did you eat? (1)
- Get off the boat! (1)
- When the rain started, all of the players left the field. (3)
- The birds sat on the wire and made a lot of noise. (4)
- Who has the green jacket and the green hat? (2)
- The tall woman wants two pairs of shoes. (3)
- “Captain Brant wants to see you right now”, she said. (1)
- Mayor Thompson cancelled the parade. (2)
- The mayor cancelled the Fourth of July parade. (2)
- That mountain range has very high peaks. (2)
- The Rocky Mountains have very high peaks. (2)
- Which book would she like to read? (1)
- The Wizard of Ox is a great book for her to read. (2)
- Seven lizards ran into the pond. (2)
- Miguel, the producer of the movie, won a big award. (4)
- The director did not win any awards. (2)
- When was the last time you went to the dentist? (2)
- Who took it and where did they go? (0)
- During the Second World War, General Patton was well known. (2)
- At the Tour de France, the riders have to be very fast. (2)
- Man of War won the Kentucky Derby in record time. (3)
- The company will ship your order today. (2)
- The rain fell on London for ten more days. (3)
- How fast will that Honda go? (1)
- How fast does your car go? (1)
- Barnum & Bailey created a large circus with many animals. (3)
- The Washington Post has a large staff of writers. (3)
- Many of the authors did not come back after lunch. (2)
- Who was that? (0)

**For a printable pdf version of the lesson, covering regular and proper nouns, click here.**

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Here’s the good news – with the right instructional design, you can do just that!

Here’s the better news – if you can follow a script, you can solve the problem!

Here’s an example lesson covering the **Final “e” Rule** in spelling.

**Click here to view and download a pdf version of this lesson – free with no obligation.**

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Click here to view and download the entire lesson, including 4 exercises and the student worksheets.

Say to the students, Now we are going to learn about fractions. Here is the first rule about fractions. We create fractions when we divide one or more things into equal parts. Listen again. We create fractions when we divide one or more things into equal parts. Say the rule about creating fractions with me. Ready. Signal.

Teacher and students say, We create fractions when we divide one or more things into equal parts.

Say the rule about creating fractions with me one more time. Ready. Signal. Teacher and students say, We create fractions when we divide one or more things into equal parts.

Say that rule on your own. Ready. Signal.

Students say, We create fractions when we divide one or more things into equal parts.

Well done. Say the rule again, Ready. Signal.

Students say, We create fractions when we divide one or more things into equal parts.

Here’s a second rule about fractions. Listen. A fraction has two parts. Listen again. A fraction has two parts. Say the rule about how many parts a fraction has. Ready. Signal.

Students say, A fraction has two parts.

Well said. Open your workbook to Lesson #1 – Exercise #1. Touch the first problem.

1 / 5

Touch the 5. Here is the third rule about fractions. The bottom part of the fraction tells us how many parts are in each group. Listen again. The bottom part of the fraction tells us how many parts are in each group.

Say the rule with me. Ready. Signal.

Teacher and students say, The bottom part of the fraction tells us how many parts are in each group.

Say the rule one more time. Ready. Signal.

Teacher and students say, The bottom part of the fraction tells us how many parts are in each group.

Your turn to say the rule about the bottom part of the fraction. Ready. Signal. Students say, The bottom part of the fraction tells us how many parts are in each group.

One more time, say the rule. Ready. Signal.

Students say, The bottom part of the fraction tells us how many parts are in each group.

Touch the number 5 on the bottom of the fraction. The number 5 tells us that there are five parts in each group. How many parts are in this group? Ready. Signal.

Students say, 5parts in each group.

Here is a picture of a fraction with 5parts in each group. Draw on the board or on a piece of paper a circle or rectangle divided into 5 equal parts.

Listen. It does not tell me how many groups there are. It only tells me that each group will have 5 equal parts.

Draw another group. If I draw another group, it must have 5parts as well. How many parts must this group have? Ready. Signal.

Students say, 5 parts in each group.

Draw 2 more circles. And how many parts must each of these two groups have?

Students say, 5 parts in each group.

Point to the 5. Does this number tell me how many parts are in each group? Ready. Signal.

Students say, Yes, 5 parts in each group.

Point to the 5. Does this number tell how many groups there are? Ready. Signal.

Students say, No.

Good job. The number 5 tells me that each group must have 5 parts, but it does not tell me how many groups there are.

Look at the next example, Q. How many parts are there in each group? Ready. Signal.

Students say, 3.

We can use circles, rectangles and even number lines to draw fractions. Draw a circle, a rectangle and a number line on the board or a piece of paper all showing two thirds.

Repeat for several examples until the students respond quickly and correctly. Have the students write the bottom number in the blank to how many parts are in each group.

Here is a whole and complete lesson for you to use for free.

This lesson uses Direct Instruction scripting to reduce frustration and confusion for the student. It also uses behavior objectives and precision teaching methods so that the student can quickly achieve fluency and mastery in the application of order of operations problems.

You can deliver each task in the lesson as a separate activity, and repeat as necessary with students. A link to a downloadable pdf with all tasks and worksheets can be found at the bottom.

Order of Operations can be confusing for students. It is much more effectively taught if we use a formula known as B.E.D.M.A.S. B.E.D.M.A.S. outlines the order in which the various steps in an order of operations math problem must be solved. The following script outlines the concepts in a step-by-step lesson.

Say to the students, “Now I am going to teach you some rules about the order of operations. The order of operations tells you the steps you must use to solve math equations. Here is the first rule. When you solve math equations, you work the problem from left to right. Listen again. When you solve math equations, you work the problem from left to right. Say that rule with me. Ready. Signal.

Students and teacher together say, “When you solve math equations, you work the problem from left to right.

Say to the students, “Say that rule all by yourselves. Ready. Signal.

Students say, “When you solve math equations, you work the problem from left to right.”

Have the students repeat the rule until they can say it quickly and accurately.

Say to the students, “New rule. My turn. Listen. When we do math problems we do each step in the correct order. Listen again. When we do math problems we do each step in the correct order. Say that rule with me. Ready.” Signal.

The teacher and students say, “When we do math problems we do each of the steps in the correct order.

Say to the students, “Say that rule with me again. Ready.” Signal.

Teacher and students say, “When we do a math problem, we do each of the steps in the correct order.”

Repeat the rule with the students until they can say it quickly and correctly.

Say to the students, “Now it is your turn to say the rule about the order of operations all by yourselves. Ready.” Signal.

The students say, “When we do a math problem, we do each of the steps in the correct order.”

Have the students repeat the rule until they can say it quickly and correctly.

Write on the board B.E.D.M.A.S. Point to the acronym and say to the students, “Here is an easy formula to remember the order of operations. Listen B.E.D.M.A.S. Listen again. B.E.D.M.A.S. Say that word. Ready. Signal.

Students say, “BEDMAS”

Say to the students, “B.E.D.M.A.S. is an acronym that tells us the order of the steps to solve a math problem. Listen again. “B.E.D.M.A.S. is an acronym that tells us the order of the steps for solving a math problem.

Say to the students, “My turn to say the rule about B.E.D.M.A.S. Listen. Each letter stands for one of the steps in the problem. Listen again. Each letter stands for one of the steps in the problem. What does each letter in B.E.D.M.A.S. stand for? Ready. Signal.

The students say, “Each letter stands for one of the steps in the problem.”

Say to the students, “My turn to say what the letters in B.E.D.M.A.S. stand for. Listen. B stands for Brackets. What does the B in B.E.D.M.A.S. stand for? Ready. Signal.

The students say, “Brackets.”

Say to the students, “That’s correct. If there are any brackets in the problem, we have to do the brackets first. What is the first step in solving the problem? Ready. Signal.

The students say, “Do the brackets first.”

Say to the students, “Next letter. The E in B.E.D.M.A.S. stands for Exponents. What does the E in B.E.D.M.A.S. stand for? Ready? Signal.

The students say, “Exponents.”

Say to the students, “That’s correct. Exponents. After we do all the brackets in the problem, we do any exponents. Listen again. After we do the brackets, then we do the exponents. What do we do first? Ready. Signal.

The students say, “We work with the brackets.”

Say to the students, “That’s correct. After the brackets, what do we do next? Ready.” Signal.

The students say, “We work with the exponents”

Say to the students, “You got it. First, we do brackets, then we do exponents. Here is the next letters. Listen. ‘D’. ‘M’. ‘D’ stands for

Division. ‘M’ stands for Multiplication. After we do the exponents, we do the division and multiplication. What do we do after the exponents? Ready. Signal.

The students say, “We work with the division and multiplication.”

Say to the students, “That’s right. After the brackets and the exponents we work with any division and multiplication. Now we have ‘B’, ‘E’, ‘D’ and ‘M’. Tell me what each letter stands for. ‘B’. Ready.” Signal.

Students say, “Brackets”

Say to the students, “ Good remembering. Next letter ‘E’. Ready.” Signal.

Students say, “Exponents”

Say to the students, “ Great. Next letter ‘D’. Ready.” Signal.

Students say, “Division.”

Say to the students, “You got it. Last letter ‘M’. Ready.” Signal.

Students say, “Multiplication.”

Say to the students, “Right again. Now lets add the last two letters of B.E.D.M.A.S. Listen. The last two letters are ‘A’ and ‘S’. What are the last two letters of B.E.D.M.A.S.? Ready. Signal.

The students say, “A and S.”

Say to the students, “Yes. ‘A’ stands for addition. ‘S’ stands for subtraction. Listen again. ‘A’ stands for addition. ‘S’ stands for subtraction. Your turn. What does ‘A’ stand for? Ready. Signal.

The students say, “A stands for addition.”

Say to the students, “Correct. ‘A’ stands for addition. What does ‘S’ stand for? Ready. Signal.

The students say, “S stands for subtraction.”

Say to the students, “That’s right. Now you know what each of the letters in B.E.D.M.A.S. stands for. Let’s review

What does the B in B.E.D.M.A.S. stand for? Ready. Signal.

The students say, “Brackets.”

Say to the students, “Next letter. The E in B.E.D.M.A.S. stands for Exponents. What does the ‘E’ in B.E.D.M.A.S. stand for? Ready? Signal.

The students say, “Exponents.”

Say to the students, “That’s correct. Exponents. What do we do after the exponents? Ready. Signal.

The students say, “Division and Multiplication.”

Say to the students, “ Good remembering. What do the last two letters of B.E.D.M.A.S. stand for? Ready. Signal.

The students say, “Addition and Subtraction.”

Say to the students, “Yes. ‘Addition and Subtraction. Nice work. Now we know the order in which we will do the steps in the problem. Let’s look at some problems and see how we solve them.

Write on the board.

5 + 7 – 4 =

Say to the students, “My turn to read the problem. Listen, Five plus seven minus four equals some number. Your turn to read the problem. Ready. Signal.

Students say, “Five plus seven minus four equals some number.”

Say to the students, “Good reading the problem. Remember the first rule about working the problem. When we work this problem do we go from right to left or from left to right. Ready.

Signal.

The students respond, “We work the problem from left to right.”

Say to the students, “Good remembering that rule. We work the problem from left to right. Look at the acronym for B.E.D.M.A.S. What is the first thing we look for in the problem?” Ready.” Signal.

Students say, “Brackets.”

Say to the students, Correct. Are there any brackets in this problem? Ready. Signal.

Students say, “No.”

Say to the students, “Right. There are no brackets. Look at the formula. What do we look for next? Ready. Signal.

Students say, “Exponents.”

Say to the students, “That’s correct. After the brackets, we look for exponents. Are there any exponents in this problem? Ready. Signal.

Students say, “No.”

Say to the students, “Right again. There are no exponents in this problem. Check your formula. What do we look for next? Ready.” Signal.

Students say, “Division and Multiplication.”

Say to the students, “You got that right as well. Are there any division or multiplication signs in this problem? Ready. Signal.

Students say, “No.”

Say to the students, “That’s right. There are no division or multiplication signs in this problem. Look at the last part of the formula. What do we look for next? Ready.” Signal.

Students say, “Addition and subtraction.”

Say to the students, “Are there any addition and subtraction signs in this problem? Ready. Signal.

Students say, “Yes.”

Say to the students, “Read the problem. Ready.” Signal.

Students say, “Five plus seven minus four equals some number.”

Say to the students, “What do we do first?”

Students say, “ Add 5 +7”

Say to the students, “That’s right. What is 5 + 7? Ready.” Signal.

Students say, “Twelve.”

Say to the students, “Right. What do we do next?”

Students say, “ We subtract 4 from 12.”

Say to the students, “What is 12 minus 4? Ready?”

Students answer, “8”

Say to the students, “Are there any steps left to do?”

Students say, “No.”

Say to the students, “Good working that problem. Let’s look at another one.

Write on the board. 6 + 9 x 3 – 12 =

Say to the students, “Read this problem. Ready. Signal.

Students read, “Six plus nine times three minus twelve equals some number”

Say to the students, “Let’s use our formula to solve this problem. What do we look for first? Ready. Signal.

The students say, “Brackets.”

Say to the students, Correct. Are there any brackets in this problem? Ready. Signal.

Students say, “No.”

Say to the students, “Right. There are no brackets. Look at the formula. What do we look for next? Ready. Signal.

Students say, “Exponents.”

Say to the students, “That’s correct. After the brackets, we look for exponents. Are there any exponents in this problem? Ready. Signal.

Students say, “No.”

Say to the students, “Right again. There are no exponents in this problem. Check your formula. What do we look for next? Ready.” Signal.

Students say, “Division and Multiplication.”

Say to the students, “You got that right as well. Are there any division or multiplication signs in this problem? Ready. Signal.

Students say, “Yes.”

Say to the students, “Remember. You work the problem from the left to the right. What do you do with the 6? Ready. Signal.

The students say, “Pass over it to the multiplication.”

Say to the students, “What do we do first? Ready.” Signal.

Students say, “We multiply 9 x 3.”

Say to the students, “That’s right. What does 9 x 3 equal?”

Students say, “27.”

Say to the students, “Perfect. 9 x 3 is 27. What do you do next? Ready.” Signal.

Students say, “Add 6 and 27.”

Say to the students, “Good remembering to work from the left to the right. What is 6 + 27?

Students say, “6 + 27 = 33.”

Say to the students, “Good work. What is the next step in this problem? Ready.” Signal.

Students say, “Subtract 12 from 33.”

Say to the students, “Absolutely. What is thirty-three minus twelve? Ready.” Signal.

Students reply, “ 21”

Say to the students, “ Have we done all of the steps? Ready.” Signal.

Students say, “Yes.”

Say to the students, “Yes. You did all of the steps. Let’s look at another problem.”

Write on the board 10 x 3 – 16 ÷ 4

Say to the students, “Read this problem. Ready. Signal.

Students read, “Six plus nine times three minus twelve equals some number”

Say to the students, “Let’s use our formula to solve this problem. What do we look for first? Ready. Signal.

The students say, “Brackets.”

Say to the students, Correct. Are there any brackets in this problem? Ready. Signal.

Students say, “No.”

Say to the students, “Right. There are no brackets. Look at the formula. What do we look for next? Ready. Signal.

Students say, “Exponents.”

Say to the students, “That’s correct. After the brackets, we look for exponents. Are there any exponents in this problem? Ready. Signal.

Students say, “No.”

Say to the students, “Right again. There are no exponents in this problem. Check your formula. What do we look for next? Ready.” Signal.

Students say, “Division and Multiplication.”

Say to the students, “You got that right as well. Are there any division or multiplication signs in this problem? Ready. Signal.

Students say, “Yes.”

Say to the students, “Remember. You work the problem from the left to the right. What do you do first? Ready. Signal.

Students say, “Divide 16 by 4.”

Say to the students, “Good work. What is 16 divided by 4? Ready.” Signal.

Students say, “16 ÷ 4 = 4”

Write on the board 10 x 3 – 4 =

Say to the students, “Nice work. 16 ÷ 4 does equal 4. What do you do next? Ready.” Signal.

Students say, “Multiply 10 x 3.”

Say to the students, “Yes indeed. What is 10 x 3?” Ready.” Signal.

Students say, “10 x 3 = 30.”

Say to the students, “You got it 10 x 3 equals 30.

Write on the board, 30 – 4 =

Say to the students, “What is the next step?” Ready.” Signal.

The students say, “We subtract 4 from 30.”

Say to the students, “ Yes. “What is 30 minus 4?”

Students say, “26”

Say to the students, “Did we finish all of the steps? Ready.” Signal.

Students say, “Yes.”

Say to the students, “Good work. Here is a more difficult question.”

Write on the board. 100 – 7² + 12 ÷ 3 =

Say to the students, “Read this problem. Ready. Signal.

Students read, “One hundred minus seven squared plus twelve divided by three equals some number.”

Say to the students, “Let’s use our formula to solve this problem. What do we look for first? Ready. Signal.

The students say, “Brackets.”

Say to the students, Correct. Are there any brackets in this problem? Ready. Signal.

Students say, “No.”

Students say, “Exponents.”

Students say, “Yes.”

Say to the students, “Right again. There are exponents in this problem. What is the exponent in this problem? Ready. Signal.

The students say, “ Seven squared”

Say to the students, “Let’s work this part of the problem. What is seven squared? Ready.” Signal.

The students say, “7² = 49”

Say to the students, “That’s right.”

Write on the board. 100 – 49 + 12 ÷ 3 =

Check your formula. What do we look for next? Ready.” Signal.

Students say, “Division and Multiplication.”

Students say, “Yes.”

Say to the students, “Remember. You work the problem from the left to the right. What do you do next. Ready. Signal.

Students say, “Divide 12 by 3.”

Say to the students, “Good work. What is 12 divided by 3? Ready.” Signal.

Students say, “12 ÷ 3 = 4”

Write on the board 100 – 49 + 4 =

Say to the students, “Nice work. 12 ÷ 3 does equal 4. What do you do next? Ready.” Signal.

Say to the students, What is the next step? Ready.” Signal.

The students say, “We subtract 49 from 100.”

Say to the students, “ Yes. What does 100 minus 49 equal?”

Students say, “One hundred minus forty nine is fifty-one”

Write on the board. 51 + 4

Say to the students, “Correct again. Did we finish all of the steps?

Ready.” Signal.

Students say, “No.”

Say to the students, “What do we still have to do?”

Students say, “Add fifty-one plus four.”

Say to the students, “Do that. How much is fifty-one plus four?”

The students say, “Fifty-one plus four is fifty-five”

Write on the board 55

Say to the students, “Have we done all of the steps. Ready.” Signal.

Students say, “Yes.”

Say to the students, “So what is 100 – 7² + 12 ÷ 3? Ready.” Signal.

Students say, “Fifty-five.”

Write on the board 36 ÷ 12 + 2(5 – 2) =

Say to the students, “This problem is more difficult. Let’s see if you can solve this one. Read this problem. Ready.” Signal.

Students read, “Thirty-six divided by twelve plus two bracket five minus two bracket equals some number.”

The students say, “Brackets.”

Say to the students, Correct. Are there any brackets in this problem? Ready. Signal.

Students say, “Yes.”

Say to the students, “Right. There are brackets. What numbers are in the brackets. Ready.” Signal.

Students say, “Five minus two.”

Say to the students, “Right. First we work with the numbers inside the bracket. What is five minus two? Ready.” Signal.

Students say, “Five minus two equals three.”

Say to the students, “That’s correct. Now we have a three inside the brackets. To get rid of the brackets we have to multiply the

number outside the bracket by the number inside the bracket. What number is outside the brackets. Ready.” Signal.

The students say, “Two”.

Say to the students. “That’s right. So what numbers do we multiply? Ready.”

The students say, “Two times three.”

Say to the students, “ How much is two times three? Ready.” Signal.

Students say, “Two times three equals six.”

Say to the students, “You got it. Now you have removed the brackets.”

Write on the board. 36 ÷ 12 + 6 =

Say to the students, “What is the next step?”

Students say, “Divide twelve into thirty-six.”

Say to the students, “That’s correct. How many times does twelve divide into thirty-six? Ready.” Signal.

The students say “Three times.”

Say to the students, “Yes, three times.”

Write on the board. 3 + 6 =

Say to the students, “What does 3 + 6 equal?”

Students say, “Three plus six equals nine.”

Say to the students, “So what does thirty-six divided by twelve plus two times five minus two equal? Ready.” Signal

Students say, “Nine.”

Task 8 – More Advanced Problem (Exponents and Brackets)

Write on the board. 6³ – 3(4) + 90 ÷ 10

Say to the students, “Read this problem. Ready.” Signal.

Students read, “Six cubed minus three bracket four bracket plus ninety divided by ten equals some number.”

The students say, “Brackets.”

Say to the students, Correct. Are there any brackets in this problem? Ready. Signal.

Students say, “Yes.”

Say to the students, “Right. There are brackets.

What do we look for next? Ready. Signal.

Students say, “We multiply the number in the bracket by the number outside of the bracket.”

Say to the students, “What numbers do we multiply? Ready.” Signal.

Students say, “Four times three.”

Say to the students, “How much is four times three. Ready.”

Students say, “Twelve”

Write on the board. 6³ – 12 + 90 ÷ 10 =

Say to the students, “What do we do next in this problem? Ready.” Signal.

Students say, “Exponents.”

Students say, “Yes.”

Say to the students, “Right again. There are exponents in this problem. What is the exponent in this problem? Ready. Signal.

The students say, “Six cubed”

Say to the students, “Let’s work this part of the problem. What is six cubed? Ready.” Signal.

The students say, “Six cubed equals eighteen.”

Say to the students, “That’s right.”

Write on the board. 18 – 12 + 90 ÷ 10 =

Check your formula. What do we look for next? Ready.” Signal.

Students say, “Division and Multiplication.”

Students say, “Yes.”

Say to the students, “Remember. You work the problem from the left to the right. What do you do next? Ready. Signal.

Students say, “Divide ninety by ten.”

Say to the students, “Good work. What is 90 divided by 10? Ready.” Signal.

Students say, “Ninety divided by ten equals nine”

Write on the board 18 – 12 + 9 =

Say to the students, “Nice work. 90 ÷ 10 does equal 9. What do you do next? Ready.” Signal.

The students say, “We subtract 12 from 18.”

Say to the students, “ Yes. What is 18 minus 12?”

Students say, “Eighteen minus twelve is six”

Write on the board. 6 + 9

Say to the students, “Correct again. Did we finish all of the steps?

Ready.” Signal.

Students say, “No.”

Say to the students, “What do we still have to do?”

Students say, “Add six plus nine.”

Say to the students, “Do that. How much is six plus nine?”

The students say, “Six plus nine is fifteen”

Write on the board 15

Say to the students, “Have we done all of the steps. Ready.” Signal.

Students say, “Yes.”

Say to the students, “So what is 6³ – 12 + 90 ÷ 10? Ready.” Signal.

Students say, “Fifteen.”

Task 9 – Order of Operation with Fractions

Write on the board. (8² – 4)

(12 ÷ 2 + 4)

Say to the students, “Read this problem. Ready.” Signal.

Students read, “Bracket eight squared minus four bracket over bracket twelve divided by two plus four.”

The students say, “Brackets.”

Say to the students, Correct. Are there any brackets in this problem? Ready. Signal.

Students say, “Yes.”

Say to the students, “Right. There are brackets. Let’s start with the brackets on the top part of the fraction. What are the numbers inside those brackets? Ready.” Signal.

Students say, “Eight squared minus four.”

Say to the students, “Can you work this problem? Ready.” Signal.

Students say, “No, we have to work the exponent first.”

Say to the students, “Good using your rule. You worked the brackets first, but you cannot do the subtraction because you have to do the exponent first. The E in B.E.D.M.A.S. comes before the S, so you have to do the Exponent before you can do the Subtraction. So let’s work the exponent. How much is 8²? Ready.” Signal.

The students say, “Eight squared equals sixty-four.”

Write on the board 60 =

(12 ÷ 2 + 4)

Say to the students, “You got that right. What do you do next? Ready.” Signal.

The students say, “ You subtract four from sixty-four.”

Say to the students, “Good job. What is sixty-four minus four? Ready.” Signal.

Students say, ” Sixty-four minus four equals sixty.”

What do we do next? Ready. Signal.

Students say, “We work with the bracket on the bottom part of the fraction.”

Say to the students, “Can we work the problem the way it is written? Ready.” Signal.

Students say, “No. We have to do the division first.”

Say to the students, “That’s correct. The D in B.E.D.M.A.S. comes before the S, so we have to do the division before we do the subtraction. What does the division problem say? Ready.”

Students say, “Twelve divided by two”

Say to the students, “How much is twelve divided by two? Ready.” Signal.

The students say, “Twelve divided by two equals six.”

Write on the board.

60

(6 + 4)

Say to the students, “What do we do next in this problem? Ready.” Signal.

Students say, “We add six plus four.”

Say to the students, “That’s correct. How much is six plus four? Ready. Signal.

The students say, “Six plus four equals ten.”

Say to the students, “Good. What do we do next?

The students say, “We divide ten into sixty.”

Say to the students, “That’s right. How much does sixty divided by ten equal?”

The students say, “Sixty divided by ten equals six.”

Say to the students, “So what does 8² – 4 equal?

(12 ÷ 2 + 4)

The students say, “Six”

Say to the students, “Nice work. That was a hard problem.

Now you are going to work the problems on the worksheet exercise. Remember to follow your formula to get each step done correctly.

A printable pdf version of the lesson including all worksheets is available for download. Click here to download the Teaching Order of Operations Complete Lesson pdf.

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