Instructors Manual

TAT2 Task 3: Instructor’s Manual

Natasha Wick

September 15, 2019

A Written Project Presented to the Faculty of the Teachers College of

Western Governors University

Table of Contents

Unit Overview……………………………………………………………….. 2

Performance Objectives……………………………………………………… 3

Materials Needed…………………………………………………………….. 4

Instructional Sequence………………………………………………………. 5

Physical Resources………………………………………………………….. 6

Daily Lesson Plans………………………………………………………….. 7-21

Lesson 1………………………………………………………….. 7

Lesson 2………………………………………………………….. 10

Lesson 3………………………………………………………….. 13

Lesson 4………………………………………………………….. 17

Lesson 5………………………………………………………….. 19

Lesson 6………………………………………………………….. 21

Assessments………………………………………………………….………. 22-25

Unit Overview

This is a 6-day math unit on solving math word problems using the CUBES method. This unit of instruction is geared for high school students who qualify for specially designed instruction and are being taught from the 6th-grade curriculum. Below you will find more details on this unit.

The instructional setting is a resource math class where 6th-grade math is being taught to high school students. The room consists of one special education teacher and 15 students. The students have varying degrees of abilities and are on different levels of understanding for math. When you have this many students who are on different levels it makes it more difficult to teach a skill in depth.

All students are given an iPad with various resources available to use. Most of the math is done via iPad and MacBooks. Manipulatives are available for many lessons and are used when students want. The classroom is small with the students gathering around two long tables allowing the teacher to walk around to every student to give guidance as needed. The students have access to the technology so they can access the curriculum as well as other resources needed to understand the math lessons.

Performance Objectives

Using a reference card, students will be able to explain the process of solving a math word problem, including each of the five components of the CUBES method in their explanations scoring a 4 out of 6.
Given a sentence with extra numbers and words, students will be able to pick out the numbers needed and what the question is to solve the equation scoring a 4 out of a 6.
Given a math word problem, students will identify what is being asked of them by identifying the math words and translating them into an equation scoring a 7 out of 9.
Given a math word problem with the wrong answer, students will accurately solve the given math word problem and will show what mistakes were made by scoring a 3/4.
Given a multi-step math word problem, students will identify all the steps and produce an equation to the problem solving for accuracy scoring satisfactorily on Math Playground.
Using Keynote, students will develop a presentation showing how they solve math word problems using the CUBE method by scoring 10/12 on the rubric.

Materials Needed

6 different multi-step math word problems with incorrect answers
CUBES reference cards
Pencil
Paper
iPad for utilizing Math Playground, Keynote, and manipulatives
Projector

Instructional Sequence

This unit will have a total of 6 lessons with each lesson lasting a little over one hour. The final lesson is a two-day lesson as it is a long process. The goal is to teach this unit during a two-week span. This allows for schedule changes due to assemblies, activities in the school, or days that the students are just not understanding. Having flexibility makes a difference with this group of kids. The lessons will start with a pre-instructional activity to get the student's minds working and wondering. The content presentation will follow allowing the students to think about the new topic as well as receive new information. Next, the learners will have an opportunity to participate in learner participation time. The students will be practicing their new knowledge to help make it more concrete. The final step will be an exit ticket that will be used as an assessment to see if the students understood the content given to them that day. The most important step will be taken in the days to follow by doing follow-through activities making sure the students are using their new skills.

Physical Resources

The three technologies chosen to include in this unit are National Library of Virtual Manipulatives, Keynote, and Math Playground.

National Library of Virtual Manipulatives will give the students the opportunity to use technology and manipulatives in one. Being able to see the manipulatives move and stack on their iPad will be an attention-getter for them. This may take a little extra time out of our day to learn how to use the online manipulatives, but the benefits will outweigh the drawbacks.
Keynote will be a fun and engaging way for students to share what they have learned by placing their new knowledge in a slide show for their peers to see. Even though this may take an entire class period, I feel like it will be an important step in their mastery of solving math word problems.
Math Playground. The students will find this to be a bit elementary for them at first but once they see how the word problems come to life and how it helps them to solve the word problems I think they will see it as a useful tool.

The technologies are all set up to help learners of all abilities to learn new material at their level. Both National Library of Virtual Manipulatives and Math Playground are geared toward the younger students based on the bright colors and animated characters, but this will be good for my high schoolers who are learning at a middle school level. Keynote will be a little more advanced as it is a presentation style. This will all be a wonderful learning experience for my students.

Lesson Plan #1 Title: What is needed and what is not.

Performance Objective: Given a sentence with extra numbers and words, students will be able to pick out the numbers needed and what the question is to solve the equation scoring a 4 out of 6.

Resources or Materials Needed: Projector, pencil, paper.

Time: 75 minutes.

Step 1: Pre-Instructional Activities: The teacher will tell a story describing the steps taken to make a pot of coffee. The story will be told with extra details, unimportant commentary, and side notes throughout. After the story is told the teacher will ask the students to share the parts of the story that were considered to be extra details, unimportant commentary, and side notes. The teacher will continue with a group discussion regarding the extra information given and talk about why it is important to recognize the extra information in a text, conversation, or even a story problem. This will engage the students in the lesson about identifying important information in a math word problem.

Step 2: Content Presentation: The teacher will project a math word problem on the board asking students to think in their heads what the question is asking. After 30 seconds the teacher will do a think-aloud while reading the question describing what the students should be thinking and doing at the same time. The teacher will then ask the students if they would have done anything differently. If someone has a different way of explaining it the teacher will allow the student to teach the class how they did it. This will go on until no other student has a question or has a concern.

Step 3: Learner Participation: The students will get into groups of 4. The teacher will put on the board a few more word problems having the students identify the important information and to identify the unimportant information. The students are to explain their reasons and explain why they agree or disagree with someone. The teacher will walk around making sure the students are giving good input, using academic language, and describing why they feel the way they do. When the groups are finished, the teacher will have the groups share with the class one of the problems they discussed and what the group came up with.

Step 4: Assessment: Students will be given an exit ticket to demonstrate what they learned. The exit ticket will have one math sentence with more numbers than are needed to make an equation. The students will have to cross out the extra numbers and write the correct equation. If students can write the correct equation I will know they understand how to decipher what information is needed and what information is not needed. Given a sentence with extra numbers and words, students will be able to pick out the numbers needed and what the question is to solve the equation scoring a 4 out of a 6.

Step 5: Follow-Through Activities: In the days to come the teacher will ask students to identify important information in a sentence. This can be as simple as placing a sentence on the board at the beginning of the period and spending 3 minutes discussing it. This will help the concept to become more concrete.

Lesson Plan Summary: This lesson plan starts off by telling a story on how to make a pot of coffee. The story has extra details, personal experiences, and unimportant information. Most of these students make and drink coffee making this story relatable. When the lesson starts the teacher is then using what they learned from the story and placing it in the math lesson. This gives the students an opportunity to build a personal understanding of a concept based on previous experiences. This follows the constructivism theory. The rest of the lesson is the students constructing their own knowledge by participating in whole group discussions as well as group discussion. They are not being told how to do it instead, they are learning how to do it together with their peers.

Assessment: Students will be given an exit ticket to demonstrate what they learned. The exit ticket will have one math sentence with more numbers than are needed to make an equation. The students will have to cross out the extra numbers and write the correct equation. If students can write the correct equation I will know they understand how to decipher what information is needed and what information is not needed. Given a sentence with extra numbers and words, students will be able to pick out the numbers needed and what the question is to solve the equation scoring a 4 out of a 6.

Lesson Plan #2 Title: Am I adding or subtracting and how do I know?

Performance Objective: Given a math word problem, students will identify what is being asked of them by identifying the math words and translating them into an equation scoring a 7 out of 9.

Resources or Materials Needed: Projector, pencil, paper.

Time: 75 minutes.

Step 1: Pre-Instructional Activities: The teacher will ask students what they remember about using academic language in past years. The teacher will use words such as add, sum, plus, increase, total, less, deduct, difference, and decrease to engage them in a group discussion. The teacher will ask the students when they might have heard these words used in everyday situations and ask for examples. These examples should be situations where the students are not in math class but instead in their everyday lives outside of school. For example, “Can you please put less cream in my coffee next time.”

Step 2: Content Presentation: The teacher will show students an anchor chart placed in the front of the classroom containing “clue words” for subtraction and addition. The teacher will read each of the words that describe subtraction and addition. The teacher will then place math word sentences on the board that contains the clue words and asks the students if they can decide what form of an equation the sentence is asking for. The teacher will show the students what happens when they pick the wrong equation and how to identify if this happens to them when they are doing independent learning. When the wrong equation is picked the answer doesn’t sound right. For example, “Tommy wanted more apples than the 2 he had so he asked his friend for 1 of his apples. How many apples does Tommy now have?” If the student came up with a subtraction equation the answer would not make sense as it would show Tommy had fewer apples than what he started with and the question clearly states he wanted more apples. This would mean an addition equation is needed.

Step 3: Learner Participation: Students will work with a partner answering 20 math word problems by identifying if it is a subtraction or addition problem then discussing why they feel the way they do. The students need proof by stating what happens if they do the wrong equation. The teacher will walk around the room to ensure the students are participating and using academic language. The teacher should make sure the students are explaining their reasoning and explaining why their reasons work or why they did not work.

Step 4: Assessment: Students will be given 4 math sentences requiring them to identify if the problem is addition or subtraction. The students will then need to identify the math word and what the translation is. Then students will have to write the equation to solve. Given a math word problem, students will identify what is being asked of them by identifying the math words and translating them into an equation scoring a 7 out of 9.

Step 5: Follow-Through Activities: In the days to come the teacher will ask students to identify math words and their translations. This can be as simple as placing a sentence on the board at the beginning of the period and spending 3 minutes discussing it. This will help the concept to become more concrete.

Lesson Plan Summary: This lesson plan starts off by linking prior knowledge to the current lesson. The teacher then shows students how using what they know about the math words and putting them in the math context can be the same thing. This is an explanation and a demonstration in one. cognitivism theory supports these techniques. During learner participation, the teacher is assisting learners in organizing the information. The teacher is guiding students to also share this new knowledge with a partner showing the new information can be readily available.

Lesson Plan #3 Title: Using CUBES to solve our problems.

Performance Objective: Using a reference card, students will be able to explain the process of solving a math word problem, including each of the five components of the CUBES method in their explanations scoring a 4 out of 6.

Resources or Materials Needed: Projector, CUBES reference cards, pencil, paper.

Time: 75 minutes

Step 1: Pre-Instructional Activities: The teacher will ask students to share out loud their experiences with solving math word problems. The teacher will have some of the sentences used from prior lessons on the board asking students to recall the math words they used and how they identified important information from the sentence. After reviewing these sentences for 5-7 minutes the teacher will begin the lesson.

Step 2: Content Presentation: The teacher will have an anchor chart displayed on the board with the CUBES method. Each student will also be receiving their own laminated card with the same CUBES method as it is printed on the anchor chart. CUBES stands for Circle important numbers, Underline the question you need to answer, Box key math words, Evaluate and eliminate unnecessary information, Solve and double-check your work. The teacher will begin with a math word problem that is grade appropriate placed on the board very large. The teacher will explain how the CUBES method works by reading the anchor chart. The teacher will then demonstrate how the CUBES method works by using illustrative examples and think aloud while solving the math word problem. This will take the teacher 5-7 minutes as the teacher will need to explain in detail what she is doing and why she is doing it all the while following the CUBES method. After the problem has been solved the teacher will place another math word problem on the board that is at a lower grade level and ask the students to help solve the problem together as a class using the same method as the teacher just used. During this time the teacher will be engaging students in deeper thinking by asking them why they chose this next step, asking if anyone has anything they would do different, why they are doing it this way, and anything else they could add to the descriptions. This will take a large amount of time to go through as the teacher will be asking the students many questions and engaging them in a lengthy discussion on the CUBES method.

Step 3: Learner Participation: The students will be placed in groups of 5. Each student will be responsible for one of the CUBES methods for example, one student will have to Circle important numbers, another student will Underline the question you need to answer, another student will Box key math words, another student will Evaluate and eliminate unnecessary information, and the fifth student will Solve and double-check their work. After all of the groups have finished the teacher will break the students up again but this time placing all “C” numbers in one group, “B” numbers in another group and so on until each group now holds the CUBES method they used together. Now the students will check their work to see if they all answered the same way. If they did not answer the same way they are to explain their answer and how they got it. This will give the students the opportunity to explain, demonstrate, and model their new knowledge. After all of the students have had a chance to share in their groups the teacher will place the same question on the board and once again explain, demonstrate, and model how to solve this math word problem using the CUBES method.

Step 4: Assessment: The students will be given a math word problem in the form of an exit ticket. They will be asked to explain each step of the CUBES method and how it is used in the given math word problem. Students must use proper academic language as well as produce the correct answer. Using a reference card, students will be able to explain the process of solving a math word problem, including each of the five components of the CUBES method in their explanations scoring a 4 out of 6.

Step 5: Follow-Through Activities: Math word problems come up on a weekly basis in our class already. It will be imperative that the teacher continues to use the CUBES method in instruction and continues to expect the students to do the same.

Lesson Plan Summary: The lesson starts off by the teacher activating prior knowledge of the student's learnings by asking the students to recall how they have been solving the math sentences this past week. The information given to students this past week has been presented in a way that the information can be stored in memory in a meaningful way. This lines up with the cognitivism theory on knowing how to organize knowledge. The cognitivism theory supports explanations, demonstrations, and modeling. Next, the teacher explains a new process on solving math word problems by demonstrating how it is used. The teacher models by solving a math word problem on the board, thinking out loud, and using academic language. Finally, the students are placed in groups where they are to solve a math word problem. The students will be asked to explain, demonstrate, and model to their peers one portion of the CUBES method. These all line up with the cognitivism theory because students will have to explain the process required to solve math word problems. Explaining will require students to understand the process not just memorize the steps. The students will show this in their assessment when they have to explain their reasoning for each step.

Assessment

The students will be given a math word problem in the form of an exit ticket. They will be asked to explain each step of the CUBES method and how it is used in the given math word problem. Students must use proper academic language as well as produce the correct answer. Using a reference card, students will be able to explain the process of solving a math word problem, including each of the five components of the CUBES method in their explanations scoring a 4 out of 6

Lesson Plan #4 Title: Where did I go wrong?

Performance Objective: Given a math word problem with the wrong answer, students will accurately solve the given math word problem and will show what mistakes were made by scoring a 3/4.

Resources or Materials Needed: 6 different multi-step math word problems with incorrect answers, CUBES reference cards, pencil, paper.

Time: 75 minutes

Step 1: Pre-Instructional Activities: The teacher will have some of the sentences used from prior lessons on the board asking students to recall the math words they used and how they identified important information from the sentence. The teacher will express how we were able to solve word problems by accurately identifying the keywords. After reviewing these sentences for 5-7 minutes the teacher will begin the lesson.

Step 2: Content Presentation: The teacher will have the anchor chart from the previous day displayed on the board with the CUBES method. Each student will also have their own laminated card with the same CUBES method as it is printed on the anchor chart. The teacher will begin with a math word problem that is grade appropriate placed on the board very large. The answer will wrong and will have to be redone to find out where the error happened to find the correct answer. This will take the teacher 5-7 minutes as the teacher will need to explain in detail what she is doing and why she is doing it all the while following the CUBES method. After the problem has been solved the teacher will show the students where the error was and how it was fixed.

Step 3: Learner Participation: The students will be placed in groups. Around the room will be different multi-step math word problems that have word shown and an incorrect answer given. The groups will have to resolve the problem by working out the CUBES method as a group. They will then have to identify where the error was made. The groups will move around the room until all 4-word problems have been solved by each group. When the students have solved every questions the groups will come together as a class and share what they found out. Each group will pick one question and share with the class their new answer and where the error occurred. If groups disagree they will have to explain why and the class will have to decide what the correct answer is.

Step 4: Assessment: The students will not be assessed on this. They will have to turn in their completed work so the teacher can see they participated as a group. The teacher will be involved in the activity so she will be able to identify if the students are understanding.

Lesson Plan #5 Title: How many steps does it take?

Performance Objective: Given a multi-step math word problem, students will identify all the steps and produce an equation to the problem solving for accuracy scoring satisfactorily on Math Playground.

Resources or Materials Needed: iPad for utilizing Math Playground.

Time: 75 minutes

Step 1: Pre-Instructional Activities: The teacher will ask the students to recall the past few days and what they have learned about solving math word problems. The teacher will allow students to talk about what they know and what they still wonder. During this conversation, other students will be able to fill in the wonder and give their peers suggestions. The teacher will ask students to share out loud their experiences with solving math word problems prior to these lessons and how they feel now.

Step 2: Content Presentation: The teacher will display on the board Math Playground for the class to see. The teacher will demonstrate what is expected during the lesson for the students to get the most out of the practice. Students are to work with a partner if they desire but only math is to be discussed. Students are to stay on Math Playground and practice multi-step math word problems until they reach a satisfactory rating.

Step 3: Learner Participation: Once the teacher has demonstrated what is expected and shown how to navigate the technology students will be allowed to work with a partner or independently if they so choose. Math Playground is a wonderful opportunity for students to get the visual of what is being asked in a math word problem while guiding students to dissect the question and solve the problem.

Step 4: Assessment: An assessment will not be given for this lesson.

Lesson Plan #6 Title: Show me what you know.

Performance Objective: Using Keynote, students will develop a presentation showing how they solve math word problems using the CUBE method by scoring 10/12 on the rubric.

Resources or Materials Needed: iPad, Projector, CUBES reference cards, Keynote.

Time: 150 minutes (2 days)

Step 1: Pre-Instructional Activities: The teacher will explain to students today is the day they will put all they have learned over the past few days to work. The teaching will be very short as to give students the opportunity to work on their presentation.

Step 2: Content Presentation: The teacher will have a presentation displayed on the board using Keynote to give the students an opportunity to see what it is. The teacher will have students open their iPad to Keynote. The teacher will give direct instructions on how to set up their presentation before allowing them to personalize it.

Step 3: Learner Participation: The students will produce a presentation via Keynote describing the CUBE steps and present it to the class.

Step 4: Assessment: The students will present their Keynote to the class describing how to use the CUBES method. Using Keynote, students will develop a presentation showing how they solve math word problems using the CUBE method by scoring 10/12 on the rubric.

Assessments

Name________________________

Directions: Cross out the extra numbers and write the correct equation. Solve the equation.

Beth is 12 years old and her sister Lou is 16 years old. They had a garage sale this summer where they made $527.25 total. The sisters want to buy new phones. Beth wants a phone that costs $250.00 while Lou wants to buy a used phone for $75.00. If the sisters were to split the money equally, how much would each sister get?

ANSWER

$527.25/2= $263.62

Directions: 1. Decide if the sentence is asking you to add or subtract.

2. Identify the math words and translate them into a math symbol.

Math sentence	add or subtract	math word = math symbol	equation
What is the sum of 404 and 217?
2. What is the difference between 22 and 49?
3. If I take away 200 apples from your 400 apples, how many apples would you have?
4. If I increase your pay of $12.22 per hour by $1.00 per hour, how much are you making per hour?

Answer Key:

Math sentence	add or subtract	math word = math symbol	equation
What is the sum of 404 and 217?	add	sum = + and = +	404+217=621
2. What is the difference between 22 and 49?	subtract	difference = -	49-22=27
3. If I take away 200 apples from your 400 apples, how many apples would you have?	subtract	take away = - from = -	400-200=200
4. If I increase your pay of $12.22 per hour by $1.00 per hour, how much are you making per hour?	add	increase = +	12.22+1=13.22

Rubric:

	1	2	3
Identify the question	The student can not identify what the question is.	The student identifies a part of the question correctly.	The student identifies all parts of the questions correctly.
Identify the math words and translates the words.	The student can not identify the math words.	The student identifies the math words but translates the words incorrectly.	The student identifies the math words and translates the words correctly.
Writes an equation	The student does not write the equation.	The student writes an incorrect equation.	The student writes the correct equation & solves the problem

Name________________________

Directions: Explain each step of the CUBES method and how it is used in this math word problems. Solve the equation.

The coffee shop has 8 indoor tables and 4 outdoor tables. Each indoor table has 4 chairs, and each outdoor table has 6 chairs. Beth and her 2 friends are trying to decide how many chairs are there in all. Can you help?

ANSWER

C- I will circle the important numbers. They are 8, 4, 4, and 6.

U - I will underline the question. The question is how many chairs are there in all.

B - I will box the important words I need to solve the equation. They are each, and in all.

E - I will eliminate unimportant information I do not need to solve the equation.

S - I will write an equation and solve to find the answer to the question.

There are 56 chairs in all.

8 x 4 = 32

4 x 6 = 24

32 + 24 = 56

Rubric

3	2	1	0
Student uses Keynote with 5 or more slides	Student uses Keynote with 3-4 slides	Student uses Keynote with less than 3 slides	Student does not use Keynote
Student uses 5 or more colors and pictures	Student uses less than 5 colors and pictures	Student uses color and no pictures	Student uses no color and no pictures
Student explains all 5 steps of CUBES	Student explains 4 steps of CUBES	Student explains 3 steps of CUBES	Student explains 2 or less steps of CUBES
Student shows enthusiasm while presenting	Student forgets some steps while presenting	Student forgets most of his presentation	Student does not present