The reason of writing this assignment is to find the problems when students do not answer the question correctly. The students are in standard 4 regarding dividing. Along with finding the students’ problems, this assignment also is to create interesting activities to make students better understand our lessons. When we have created interesting lesson plans it is hoped that the students will become interested to learn mathematics. This writing takes example from sample question paper from standard four students.
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Error1: Does not understand the concept or question requirements and the terms used.
The hardest thing about doing word problems is taking the English words and translating them into mathematics. Usually, once students get the math equation, they are fine; the actual math involved is often fairly simple. But figuring out the actual equation can seem nearly impracticable. What follows is a list of hints and helps. Be advised, however: To really learn "how to do" word problems, students will need to practice, practice, practice.
Division is splitting into equal parts or groups. It is the result of "fair sharing", for example: there are 12 chocolates, and 3 friends want to share them, how do they divide the chocolates? Answer: They should get 4 each. We use the ÷ symbol, or sometimes the / symbol to mean divide:
12 / 3 = 4
12 ÷ 3 = 4
The question requires the students to answer by dividing, but the students answer by multiplying , addition and subtracting. The example of the error is visible in paper no 4, set no 2, on question no 4. students also do not understand what the question means, although the question is in both languages. They also do not understand the technical terms, when it is presented as a case study, then they cannot understand it. They are able to solve the problems when they are presented in numbers only.
Error 2: Do not complete the worksheet.
Students understand the question requirement where they perform the divide operation, but the problem happens when the operation is not complete. They do it halfway and they arrive to an incomplete answer. They assume that the work task is already complete, and they actually are in the middle of the operation, but they stop the task. Along with that, they are lazy to calculate and solve operations that involve number in hundreds. Sample of questions are like set 1, question 1 and 2, second set of question 3 and set 4, question no 1.
Error 3 : Students do not know how to solve problems the normal way.
The students understands the question requirements but do not know how to solve in a normal way.
They do change to the normal way in order to arrive at the correct answer. Instead, they take the easier way, that is they use the (÷) symbol and write 233÷5= or 235/5= and not solve in horizontal or normal manner, and that makes them to arrive at the wrong answer. The students write the answers as they want it to. The error is visible to all question sets.
Error 4: Error in subtraction
The students understand the question’s requirements that is subtraction, they can solve it in a normal way, but the problem arises when they perform the subtraction process to get the results. The students subtract a smaller number with a bigger number. They will turn the number arrangement upside down, where the number to be subtracted is below the number that is subtracting. For example: 34-43=?, which is wrong.
The problems need to be broken down into a few solutions. This is to avoid the students become confused when performing the task. While the task is done, the teacher explains the steps taken.
Improvements for Error 1: Students not able to understand the terms used
The first step to effectively translating and solving word problems is to read the problem entirely. Tell students do not start trying to solve anything when they only read half a sentence. Try first to get a feel for the whole problem; try first to see what information it has.
The second step is to work in an prepared manner. Figure out what you need but don't have, and name things. Pick variables to stand for the unknown, clearly labelling these variables with what they stand for. Draw and sticker pictures neatly. Explain the reasoning as students go along make sure they know just exactly what the crisis is actually asking for. Students need to do this for two reasons: Working clearly will help them think clearly, and figuring out what they need will help you translate your finishing answer back into English.
It can be really annoying to spend fifteen minutes solving a word problem on a test, only to realize at the end that you no longer have any thought what "x" stands for, so you have to do the whole problem over again
The students are given the keywords, teacher stresses on the key words such as difference, balance and remainder, plus and addition, equal sharing, grouping involving dividing and altogether. They are shown examples of case studies related to the usage of the keywords. They are also given more exercises to crack the problems, to familiarize the students with problem solving. The students underline the keywords in the question so they can see clearly the question’s necessities.
There are special names for each number in a division: dividend ÷ divisor = quotient. Let us look at the example, 12 is the dividend, 3 is the divisor and 4 is the quotient.
Improvements for Error 2: Students do not complete the worksheet.
The students are given simple and straightforward questions so they can complete the worksheet. After that, when they have succeeded in completing the task, difficult questions, such as case study will be given. They are reminded to complete the questions and not to skip any step. Teacher can monitor the student’s achievements
Improvements for Error 3: Students do not know how to solve problems the normal way.
The students are asked to change the question format into the normal method of answering. To make them easy to answer, they perform the task in front of the class, and teacher corrects their mistakes. The students are also shown the symbol for dividing, that is the shape of a rooftop, or 7 in a horizontal manner. They are given more exercises and using the method that I have devised, they are guided step by step on how to change the question format, from ÷ to
Improvements for Error 4:Students subtract smaller to bigger numbers
Remind the students that to subtract, the bigger number must be on top of the smaller and simple number. Students also must know they have to subtract downwards when performing the dividing process. They are given simple subtraction exercises, and teacher checks on their mistakes when they carry out the task. They are given simple dividing such as 34/5=
They have to arrange numbers in a standard way, so they are able to subtract 34-30 in the first step. They also are shown that simple mistakes to subtract, like subtracting upwards when dividing must not happen. For example; 34-35=1, and it should be 35-34=1
Activity for error 1: Does not understand the concept or question requirements and the terms used.
- Teacher reminds students on selecting the correct concept to answer question .
(Written on cue cards, these words are shown to the students: difference, balance and remainder, plus and addition, equal sharing, grouping involving dividing and altogether. Then, they are shown a solution that involves the usage of the technique. The students tell teacher what operation is involved.)
- Teacher shows a cue card containing a question: 25/5=
- Teacher asks: What is the operation involved and students answer: Divide
- Teacher shows another cue card containing a question: Salleh has 8 marbles. He buys another two for his collection and asks: What is the operation involved ?
- Students answer: Addition. If the students answer, teacher asks how do they arrive at the answer. Teacher: Wht do you say the problem needs addition ? Student: It is because the question says … ‘for his collection’.
Teacher gives set of question related to the terms and definitions, they match the phrases or terms with the terms used. The students are shown the sample case study and they find the phrase below. Then they show the sign to teacher.
- Pours equally into
- Gives equally to
- Distributes equally to
- Given equally into
- Donates equally to
Minus, or subtraction
- Ahmad lost his marbles …
- Somebody stole the cats…
- He eats 3 muffins …
- One boy goes home and leaves his friends …
- One cat gave birth to three kittens ..
- His parents gave him more money …
- I write more sentences…
- times, multiplied by
- product of
- increased/decreased by a
- factor of
The activity to settle the problem is they are given 5 questions along with cards. In the cards, there are numbers, symbols and lines. They must arrange all the cards in order to solve the maths problem . Each maths problem has different set of cards. Teacher tells students which cards are to be used for a particular question.every question needs a different set of numbers and symbols altogether, and the students arrange the cards until all the cards have been used.
Activity for error 2: Students do not complete worksheet.
Teacher prepares cue cards with numbers, symbols and lines. These cards are cut. Example:
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These cards are what is required to be used in order to solve 5 maths problem related to dividing. These are the 5 problems:
Each maths problem uses a different amount of numbers, so they have a different set of cards from each other. Teacher tells students which cards are to be used for a particular question. The students arrange the cards until all the cards have been used.
The students are given this question and the number cards that will be used to solve the problem, What is the sum for 247/3 ?The cards are one card containing number 8, 2 cards containing number 4, 3 cards containing number 1, one card containing number 3, 2 cards containing number 2, two cards containing line and a card containing the letter r. This letter represents ‘remainder’. All these cards must be used, including the remainder card, because there will be a remainder or a balance, that is 1.
1. Students are given time to arrange all the cards given in order to solve 5 maths problems using the normal way.
2. When they have finished the first question, the answers are discussed one by one.
3. The first question and the method to solve the normal way is written on the board.
4. They are shown the method, step by step.
5. The students checks how they arrange the numbers and symbols.
6. If there are errors, they rearrange the numbers.
7. The lesson is concluded.
The teacher is equipped with the table, where the amount of numbers and symbols involved in an operation is mentioned. In the first question, 514÷5, it involves 1 unit of the number 7, 3 units of number 2, 2 units of number 2, 4 units of number 1, 1 unit of number 1, 1 unit of number 9, and one r letter used. R here stands for remainder.
In the second question, that is 402 ÷ 7, teacher prepares 2 units of number 6, 2 units of number 2, 2 units of number 4, 1 unit of number 7 and 1 unit of zero.
Question number 3, teacher prepares 2 unit of number 4, 2 units of number1, 3 units of number 2, 1 unit of number 5 and one r letter.
In the fourth question, each groups are given 1 unit of number 9, 3 units of number 6, 2 units of number 1, 1 unit of number 4, 1 unit of number 3 and one unit of number zero.
In the fifth question, which is the last question, each group will get 2 units of number 4, 1 unit of number 2, 4 units of number 6, 3 units of number zero, 1 unit of number 5, 1 unit of number 8 and one unit of line.
- 514÷ 7
Activity for error 3: Students do not know how to solve problems the normal way.
The students are given a straightforward question, and not case study and they answer one by one so they understand the correct method. They have to arrange the numbers so the numbers are presented correctly.
1) Students are gathered into groups of five. They are given cards that have a number for each card. All the numbers that are given must be used, there are no extra cards given.
2) They are given a case study, and they solve the maths problem using the normal method. For example, they are given 2640 / 12.
3) They are given 5 cards containing a zero number each, 5 cards containing the 2 number each, and three cards, each has 4 number. They are given the subtraction symbol (-) three cards.
4) Teacher will ask students to show the arrangement and the answers of the questions.
Cut out the cards
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Give questions that require a single or a number of zeros at the end of the answer.
- 4000 /4 =
Ask them to arrange the numbers according to the normal method.
Activity for error 4: Students subtract smaller to bigger numbers
- The students are reminded that a small number can be used as a subtraction number for a bigger number. How can we subtract a one-digit number from a two-digit number, mentally? If we subtract the other way around , then it is impossible to manage it.
- They are taught on how to break off from the smaller number the ones digit of the larger (2), and subtract to get a multiple of 10. In this case, they are given a number that is 522. Then, they break 522 and it becomes 50.
- Then they subtract the rest of the smaller number and it becomes 501 = 49.
- Teacher shows the example of the working as below.
Example 4. Calculate mentally 83 − 5.
Solution. "83 minus 3 is 80; minus 2 is 78."
Example 5. Calculate mentally 72 − 6.
Solution. "72 minus 2 is 70; minus 4 is 66."
Example 6. A book has 195 pages, and you have read 7 of them. How many pages are left?
Answer. "195 minus 5 is 190; minus 2 is 188."
It is hoped that with the workings sample, the students under the study will assist the findings, where are the areas needed to be improved. Such methods which need to be improved from time to time, is necessary in order for the future children to be able to learn division properly, and reduce the mistakes.