Solving Linear Equation Word Problems (40 mins)

Objectives

Students will be able to solve linear equation word problems by themselves.

Students will have a chance to appreciate the application of linear equation in daily life.

Motivation tip: Many students find topics on algebra and equations abstract and has nothing to do with daily life. Textbook examples are not always satisfactory in addressing this issue. As solving equations involves finding an unknown x of a problem, teacher may channel this through some unknowns that students are interested to know, such as the age of the teacher themselves, and then make up a word problem as a set for the face-to-face lesson, or the question to be asked among the pre-learning videos.

Before-class (On-line)

Teacher look for basic explanation videos which suits their students from YouTube or other sources, or create the necessary explanation videos by themselves using tools such as Explain Everything, Clips etc.
Lesson design thinking: The difficulty of the pre-learning video content should be somehow similar to the level 1 problems in common textbook. That is, students self-learn basic and foundation concepts in the pre-learning stage at home (private learning space).
More difficult or level 2 problems should be left to face-to-face lessons, simply because even higher ability students will have problems, then teacher can provide support to students through face-to-face interactions. Imagine if more difficult problems are put on-line for students to solve, it will be quite hard for teachers to do support.
Teacher put the videos in the Learning Management System (LMS) they preferred, and curate a follow-up question (preferably close end questions which facilitates LMS auto-marking) for each video.
Teacher instructs students to watch the videos on-line and answer the question that follows before the face-to-face lesson. The LMS will do the auto-marking if closed end questions are used. Teacher can then just look at the report and statistics (pre-learning analytics) and find out who has not pre-learned and which question is not well-answered.

Word problem (Mother and daughter's age)

Word problem (Black and white balls)

How to solve word problems

Pre-learning Analytics from LMS

Learning data captured by LMS are very useful for teacher to diagnose self-learning ability of the whole class.

Teacher has to check these data before attending the face-to-face lesson with students.

First of all, for students who have not pre-learned, teacher have to take action to cope with them, which can be quite school-based or teacher-based.

Learning analytics (view by question)

View by question is a common feature provided by LMS in a quiz setting. Teacher can find out directly which question is not well-answered by going through the question statistics. Such questions are the content that students cannot understand or pre-learn by themselves.

Teacher need to give support to students by using the first 5 to 10 minutes in the face-to-face lesson and re-explain the solution to the question.

LMS Auto-marking results page

Depending on the LMS teachers are using, some will even provide an auto-marking result page for every student and every question. If this function is available, teachers can find out the common mistakes and patterns made by the whole class before the face-to-face lesson.

This is exactly where the huge benefit of flipping classroom lies, teachers have already know a lot about students' learning before class and therefore adjust teaching behaviour and strategies accordingly.

Requesting pre-learn-less students to complete the pre-learning tasks during lunch time or after school in the computer room is effective in building the habit of self-learning and responsibility of students.

In-class face-to-face Lesson (Tutorial style 40 mins)

Teacher give printed paper notice to pre-learn-less students that they have to complete the pre-learning tasks in the computer room during lunch time or after school. (1 mins)
Teacher re-explain to the whole class the solution of pre-learning problems with the lowest correct percentage. (4 mins)
Teacher deliver worksheet to students (ask students to work in groups if necessary) and ask them to complete it in class, based on the basic knowledge they have pre-learned last night. (25 mins)
Student are allowed to discuss with each other and they may raise up their hands to ask any time as the teacher is now free to provide support any time (instead of doing direct teaching and explanation all the time as in a traditional classroom setting). The teacher is now playing the role of a "tutor", instead of a "teacher", and the classroom setting becomes a tutorial centre or homework clinic.
The difficulty level of the worksheet should be higher than the pre-learning materials, such as incorporating the level 2 problems from the textbook. The design thinking is, if students got 25 minutes of doing homework in class, how many level 2 problems should be assigned? Note that the considerations is the majority of students can complete without asking too many questions that overwhelm the only teacher/tutor in the classroom.
10 minutes before the lesson ends, teacher ask student representatives to work out the solutions on the blackboard so that everyone in the class can have a check and reference. The student representatives may be chosen from groups assigned by teacher or students just organize by themselves. Students are also instructed to check and mark their own solutions against those written on the blackboard, which may or may not be correct at all. The teacher can then review, comment, ask, consolidate the solutions on the blackboard to the whole class. (10 mins)
At the end of the lesson, the teacher collect all the worksheets from the class to have a final review. Depending on whether the teacher has got the extra time, the worksheets can be effectively marked afterwards because the solutions have been walked through in the class.

3.3 Word problems.pdf

Sample student worksheet (Word problems on solving linear equations)

3.2c Equations Fractions.pdf

Sample worksheets completed by students (from another section of the same chapter)

The traditional blackboard is an effective tool for consolidation and review of solutions to the "homework" problems.

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Solving Linear Equation Word Problems (40 mins)

Objectives

Students will be able to solve linear equation word problems by themselves.

Students will have a chance to appreciate the application of linear equation in daily life.

Before-class (On-line)

Teacher look for basic explanation videos which suits their students from YouTube or other sources, or create the necessary explanation videos by themselves using tools such as Explain Everything, Clips etc.

Lesson design thinking: The difficulty of the pre-learning video content should be somehow similar to the level 1 problems in common textbook. That is, students self-learn basic and foundation concepts in the pre-learning stage at home (private learning space).

Teacher put the videos in the Learning Management System (LMS) they preferred, and curate a follow-up question (preferably close end questions which facilitates LMS auto-marking) for each video.

Word problem (Mother and daughter's age)

Word problem (Black and white balls)

How to solve word problems

Pre-learning Analytics from LMS

Learning data captured by LMS are very useful for teacher to diagnose self-learning ability of the whole class.

Teacher has to check these data before attending the face-to-face lesson with students.

First of all, for students who have not pre-learned, teacher have to take action to cope with them, which can be quite school-based or teacher-based.

Learning analytics (view by question)

View by question is a common feature provided by LMS in a quiz setting. Teacher can find out directly which question is not well-answered by going through the question statistics. Such questions are the content that students cannot understand or pre-learn by themselves.

Teacher need to give support to students by using the first 5 to 10 minutes in the face-to-face lesson and re-explain the solution to the question.

LMS Auto-marking results page

Depending on the LMS teachers are using, some will even provide an auto-marking result page for every student and every question. If this function is available, teachers can find out the common mistakes and patterns made by the whole class before the face-to-face lesson.

This is exactly where the huge benefit of flipping classroom lies, teachers have already know a lot about students' learning before class and therefore adjust teaching behaviour and strategies accordingly.

Requesting pre-learn-less students to complete the pre-learning tasks during lunch time or after school in the computer room is effective in building the habit of self-learning and responsibility of students.

In-class face-to-face Lesson (Tutorial style 40 mins)

Teacher give printed paper notice to pre-learn-less students that they have to complete the pre-learning tasks in the computer room during lunch time or after school. (1 mins)

Teacher re-explain to the whole class the solution of pre-learning problems with the lowest correct percentage. (4 mins)

Teacher deliver worksheet to students (ask students to work in groups if necessary) and ask them to complete it in class, based on the basic knowledge they have pre-learned last night. (25 mins)

At the end of the lesson, the teacher collect all the worksheets from the class to have a final review. Depending on whether the teacher has got the extra time, the worksheets can be effectively marked afterwards because the solutions have been walked through in the class.

Sample student worksheet (Word problems on solving linear equations)

Sample worksheets completed by students (from another section of the same chapter)

The traditional blackboard is an effective tool for consolidation and review of solutions to the "homework" problems.