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"Everyone’s Got (Word) Problems" Grades 6th to 9Th

This lesson uses the four modalities of reading (reading, writing, listening, and speaking) on a math word problem to bridge the gap between reading and math.
BIlly Edward Bush B.A, M.Ed.
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What's included

8 live meetings
8 in-class hours
Homework
1 hour per week. Homework Students will be given worksheets to compete and be prepared to have discussions at the start of the next class.
Assessment
Students will be given a Summative Assessment assignment. The assessment is designed to reinforce the concept of reading and breaking down Math word problems. If students struggle with the assignment, I will be made aware of misunderstandings, and shortcomings of the lesson taught. When "weak" areas are identified on the assignment, I can address during the next available class period and will have students take a short online practice on a fun and interactive website.

Class Experience

US Grade 6 - 8
How will students learn? 

There will be several ways to interact with me in an online class: through synchronous interaction and asynchronous interactions.

Here are some examples of ways I will engage in synchronous interactions:

Live course orientation. 

Synchronous online meeting. 

How will the students learn?

*The students will be able to discuss what makes word problems challenging. Explain that one strategy for solving
word problems effectively is to identify “key words” which indicate a mathematical operation. 

How will they interact with myself and each other?

I will use the gradual release method of teaching: " I do, we do, you do" 
- First, I demonstrate how to do it (using several examples).  
- Next, the students do some problems along with me.
- Finally, they complete some problems on their own that I will check for accuracy and give more guidance if needed. 

How is class time structured?

The material taught in an online course follows a structure. Just like a traditional course, students start at the beginning of the education objectives and progress through the coursework. They move from the most introductory topics the class covers to the most advanced.

What topics will be covered?

Students will be able to master the following in this lesson: 

Listed below are some of the questions that you may ask during this lesson and what they need to master. The questions I will ask will depend on the students' responses. My focus in this part of the lesson is to have students try and picture the problem in their head and creating a graphic organizer template to make sense of what is happening in any given Math problem. Students will come up with a variety of answers. Some example questions I could ask include:

1) What do you notice about this word problem? (answers may vary: there are 8 zebras and 5 monkeys, it has animals, it has numbers, etc.)
2) What is different in the problem? (answers may vary: there are different animals, numbers are different, there's more zebras, there are less monkeys, etc.)
3) What are we trying to find out? (how many less monkeys there are than zebras)
4) How can we represent this part of the story? (draw, write a number, use manipulatives)
5) What would help us organize our thinking and our work? (answers may vary: draw it out, act it out, write an equation, etc.)
6) What strategies can we use to solve this problem? (we can match up 5 zebras and 5 monkeys then see how many zebras are left, that will tell us how many fewer monkeys we have than zebras.)

Class break down per day of instruction. Note *(instructional minutes may vary depending of skill set of students/groups)

Introduction and Rationale
Throughout these lessons I will be building the students skills and knowledge of multiplying and dividing fractions. 

 Day #1 (60 minutes)*

1) Before beginning the lesson, Students will take out Word Problem Papers (below, 4 in all) around the
room.
2. On my computer screen I will write the words Addition, Subtraction, Multiplication, and Division.
3. Ask students to brainstorm words that mean addition, subtraction, multiplication, and
division. Call on students to participate and write words on the shared computer scree under the
appropriate category. (For example, students may say “times,” this would be written
under the multiplication category).
4. Give students a sample word problem and ask them what the key word is in the
problem. (For example, “Janelle and Maria went on a trip together. They spent a
total of $550.00. They split they expense equally. How much did each spend?”
Students should recognize the words “split” and “each” as key words which indicate
division.)
5. Repeat above with other sample word problems.
6. Ask students to write down categories and word from the computer screen.
7. Separate students into independently will be assign each to a Word
Problem Paper given to them and share with the group of students. 
8. Explain that they will be given one minute to identify the key words and mathematical
operations in each problem on the computer screen. Emphasize that they DO
NOT have to solve the problem, but only identify the key words and mathematical
operations.
9. Set timer for one minute. Encourage individuals to work at the highest level they can do. 
10. At the end of one minute, students will enter their answers on the computer screen by sharing the control of the screen. 
Continue until each student has rotated to each set of questions.

Homework 
Students will be given worksheets to compete and be prepared to have discussions at the start of the next class. 

Day #2 (60 minutes)*

"1. Watch a math video relevant to what I am teaching. This lesson will most effective when it is used within the Operations strand (addition, subtraction, multiplication and division) but could also work for Geometry (finding the circumference of circle, the volume of a sphere), Statistics (Mean/median/mode), and other areas of math.

2. After the video, have students answer the Challenge Questions and complete any associated printable exercises.

3. Create a sample word problem that utilizes the type of math operation you’re focusing on. Walk through the problem with the class, pointing out the importance of reading it carefully (and aloud if helpful), understanding what you’re solving for, and underlining the most relevant information to help guide the problem solving process.

4. Students will explain that they are going to create word problems for each other to solve. Tell them that they can be as silly or creative as they want them to be, but lay down any parameters you feel are necessary (how long they have to be, how many steps they have to include, minimum/maximum value of numbers used).

5. Students should be given a certain amount of time to complete their problem (and have the answer themselves).

Wrap Up/Extensions

-Students can work to create a third word problem.

-Optional: Give the students the answer to the problem and they then have to create the word problem that will lead there.

-Optional: Students can create whole stories/narratives that have a word problem at the center. They can write these with a younger audience in mind and then share them with their parents. 

Guided Reflection
-"I used to think ______ and now I think ______"
-"One thing I learned is ________________ and one question I still have is _________"

Homework 
Students will be given worksheets to compete and be prepared to have discussions at the start of the next class. 


Day #3 (60 minutes)*
Activate prior knowledge by displaying the following word problem:

Sam wants to buy a new car before he goes to college. His parents said they would pay for half. Sam has been comparing prices and thinks he will find the perfect college vehicle for $18,990. Sam finds a great job sacking groceries at a nearby store making $7.25 per hour. If Sam works 20 hours per week, how long will it take him to save enough money for the car?

Give students 5 minutes to solve the problem on their own and to come up with an explanation for their answer. Have students write this information on a sticky note and place it on the corner of work space.

Each individual student will take out a sheet of lined paper. Have students fold the chart paper in half and then fold it in half again. Have students label the top of each section with the following:

Visualize Problem
Write Equation
Solve Equation
Explain Answer

Continue watching part of 'A Multiple-Step Word Problem' section. Pause at the 2:16 mark. Have students refer back to the word problem about Sam's new car. In the 'Visualize Problem' section of their chart paper, have each students create and label a cartoon that clarifies what the word problem is asking and what pertinent information the word problem provides.

Give students another sticky note and 2 minutes to adjust their original solution to this problem if necessary. Have students add a note explaining any changes to their original answer. Have students keep all of their sticky notes to show progression in learning.

Continue watching the remainder of 'A Multiple-Step Word Problem' section. Pause at 3:55.

Have students work independently to write an equation that represents Sam's new car word problem in the 'Write Equation' section of their chart. Students take out a sheet of paper  to make any corrections to their solution.

Briefly review order of operations with students. Then, watch the remainder of the video.

Have students solve their equation and explain their answers in the third and fourth sections of their chart paper. Provide students an opportunity to share their completed chart with you or others. Discuss any challenges and give students the opportunity to correct their mistakes.

Discussion Questions
Why do you think people are sometimes afraid of word problems?
What would you say to make them feel better about word problems?
Why is visualization an important first step in solving word problems?
Why do you need to know about the order of operations?

Day #4 (60 minutes)*

Class review and assessment

During this class students will be allowed to have an open discussion on what problems or success they experienced as well as to practice more in-depth questions. 

Students will be given a Summative Assessment assignment. The assessment is designed to reinforce the concept of multiplying  and dividing fractions. If students struggle on the assignment, I will be made aware of misunderstandings, and shortcomings of the lesson taught and relay information to parents to support all stake holders.

Lesson Extension
Have students create their own multi-step word problem and solve the problem on poster or chart paper, clearly showing each solution step. For a collaborative element, ask students to create word problems for their peers to solve.
Common Core Standard(s): 

CCSS.MATH.CONTENT 7.NS.1d. 
7.NS.1d.  Apply properties of operations as strategies to add and subtract rational numbers.

CCSS.MATH.CONTENT.8.EE.7b
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

CCSS.MATH.CONTENT.7.EE.4
Use variables to represent quantities in a real-world or mathematical problem and construct simple equations and inequalities to solve problems by reasoning about the quantities.

CCSS.MATH.CONTEN 6.NS.C.5:
6.NS.C.5: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values; use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

CCSS.MATH.CONTEN 6.NS.A.1
6.NS.A.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.
Learning Goals
Guiding Questions: What are the guiding questions for this lesson?
Listed below are some of the questions that you may ask during this lesson. The questions you ask will depend on the students' responses. The teacher's focus in this part of the lesson is to have students try and picture the problem in their head and make sense of what is happening in this problem. Your students will come up with a variety of answers. Some example questions you could ask include:

Here are the seven strategies I use to help students solve word problems.

1. Read the Entire Word Problem
Before students look for keywords and try to figure out what to do, they need to slow down a bit and read the whole word problem once (and even better, twice). This helps kids get the bigger picture to be able to understand it a little better too.

2. Think About the Word Problem
Students need to ask themselves three questions every time they are faced with a word problem. These questions will help them to set up a plan for solving the problem.

Here are the questions:

A. What exactly is the question?
What is the problem asking? Often times, curriculum writers include extra information in the problem for seemingly no good reason, except maybe to train kids to ignore that extraneous information (grrrr!). Students need to be able to stay focused, ignore those extra details, and find out what the real question is in a particular problem.

B. What do I need in order to find the answer?
Students need to narrow it down, even more, to figure out what is needed to solve the problem, whether it's adding, subtracting, multiplying, dividing, or some combination of those. They'll need a general idea of which information will be used (or not used) and what they'll be doing.

This is where key words become very helpful. When students learn to recognize that certain words mean to add (like in all, altogether, combined), while others mean to subtract, multiply, or to divide, it helps them decide how to proceed a little better

Here's a Key Words Chart I like to use for teaching word problems. The handout could be copied at a smaller size and glued into interactive math notebooks. It could be placed in math folders or in binders under the math section if your students use binders.

One year I made huge math signs (addition, subtraction, multiplication, and divide symbols) and wrote the keywords around the symbols. These served as a permanent reminder of keywords for word problems in the classroom.

C. What information do I already have?
This is where students will focus in on the numbers which will be used to solve the problem.

3. Write on the Word Problem
This step reinforces the thinking which took place in step number two. Students use a pencil or colored pencils to notate information on worksheets (not books of course, unless they're consumable). There are lots of ways to do this, but here's what I like to do:

Circle any numbers you'll use.
Lightly cross out any information you don't need.
Underline the phrase or sentence which tells exactly what you'll need to find.

4. Draw a Simple Picture and Label It
Drawing pictures using simple shapes like squares, circles, and rectangles help students visualize problems. Adding numbers or names as labels help too.

For example, if the word problem says that there were five boxes and each box had 4 apples in it, kids can draw five squares with the number four in each square. Instantly, kids can see the answer so much more easily!

5. Estimate the Answer Before Solving
Having a general idea of a ballpark answer for the problem lets students know if their actual answer is reasonable or not. This quick, rough estimate is a good math habit to get into. It helps students really think about their answer's accuracy when the problem is finally solved.

6. Check Your Work When Done
This strategy goes along with the fifth strategy. One of the phrases I constantly use during math time is, Is your answer reasonable? I want students to do more than to be number crunchers but to really think about what those numbers mean.

Also, when students get into the habit of checking work, they are more apt to catch careless mistakes, which are often the root of incorrect answers.

7. Practice Word Problems Often
Just like it takes practice to learn to play the clarinet, to dribble a ball in soccer, and to draw realistically, it takes practice to become a master word problem solver.
learning goal

Other Details

Supply List
Print out of the attaches included in this lesson
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External Resources
In addition to the Outschool classroom, this class uses:
  • Kahoot
Joined March, 2020
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Teacher expertise and credentials
California Teaching Certificate in Elementary Education
California Teaching Certificate in Mathematics
Master's Degree in Education from Claremont Graduate University
I am a California certified teacher with multiple degrees and certifications  (B.A., M.Ed, Ed.D in Educational leadership, ESOL, GLAD, and AVID) who has taught Middle school and Upper Elementary school for 15 years and I have been teaching mathematics to homeschoolers from grades k-12, both in-person and online for over 6 years.  I always wanted to be a teacher, and I am living the dream!  Also, I cater to students who struggle with or do not care for math. I say this because Algebra is critically important because it is often viewed as a gatekeeper to higher-level mathematics and it's a required course for virtually every postsecondary school program.  I have 6 basic reasons why I think offering this class is so important.  

1) Algebra is Faster And Better Than “Basic” Math
Just as multiplying two by twelve is faster than counting to 24 or adding 2 twelve times, algebra helps us solve problems more quickly and easily than we could otherwise. Algebra also opens up whole new areas of life problems, such as graphing curves that cannot be solved with only foundational math skills.

2) Algebra is Necessary to Master Statistics and Calculus

While learning one kind of math to learn more kinds of math may not be an immediately satisfying concept, statistics and calculus are used by many people in their jobs. For example, on my other side job as a research person for a local non-profit organization, I use statistics every day. I help departments identify ways to measure their success. In general, statistics are used in certain jobs within businesses, the media, health and wellness, politics, social sciences, and many other fields. Understanding statistics makes us wiser consumers of information and better employees and citizens.

Calculus helps us describe many complex processes, such as how the speed of an object changes over time. Scientists and engineers use calculus in research and in designing new technology, medical treatments, and consumer products. Learning calculus is a must for anyone interested in pursuing a career in science, medicine, computer modeling, or engineering.

3) Algebra May Be a Job Skill Later

A student may be confident they are not going into any career needing statistics or calculus, but many people change jobs and entire careers multiple times in their working life. Possessing a firm knowledge and understanding of algebra will make career-related changes smoother.

4) Algebra Can Be Useful in Life Outside of the Workplace

I have found algebra helpful in making financial decisions. For example, I use algebra every year to pick a health care plan for my family using two-variable equations to find the break-even point for each option. I have used it in choosing cell phone plans. I even used it when custom-ordering bookshelves for our home. 

5) Algebra Reinforces Logical Thinking

I would not use algebra as the only means of teaching logic. There are more direct and effective means of doing so, but it is a nice side-benefit that the two subject areas reinforce one another.

6) Algebra is Beautiful

The beauty of algebra is an optional benefit because one has to truly choose to enjoy it, but algebra provides us with a basic language to describe so many types of real-world phenomena from gravity to the population growth of rabbits. That five letters can be used to describe how an entire category of matter, namely ideal gases, behaves is amazing and beautiful in its simplicity.

There is also a beauty when we start with a complex-looking problem and combine and simplify over and over until we have one value for each variable. The process can be enjoyable and the result immensely satisfying.

Algebra is an important life skill worth understanding well. It moves us beyond basic math and prepares us for statistics and calculus. It is useful for many jobs some of which a student may enter as a second career. Algebra is useful around the house and in analyzing information in the news. It also reinforces logical thinking and is beautiful.

So, keep an open mind about why we learn algebra and look for ways to share its applications with students. Dispel the stigma that it is a boring list of rules and procedures to memorize. Instead, consider algebra as a gateway to exploring the world around us. Those are our top reasons why we learn algebra, and there are plenty more. 

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$155

weekly or $310 for 8 classes
4x per week, 2 weeks
60 min

Completed by 265 learners
Live video meetings
Ages: 12-14
1-18 learners per class

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