TITLE: Multi-digit dividends

AUTHOR: Teacher’s name

GRADE LEVEL/SUBJECT: Appropriate for grade 5

OVERVIEW: Understanding division in all its aspects (from simple operation to properties and connection with multiplication) can be difficult for many students. It takes time and practice in order to can use it further in algebra, geometry, trigonometry or calculus. Also the practical part is very important for using division confidently in real life.

OBJECTIVE(s): The students will be able to:

1. Accurately divide multi-digit numbers;

2. Accurately understand and use division’s property of being distributive;

3. Accurately understand the relation between division and multiplication; check the correctness of the division using the multiplication

RESOURCES/MATERIALS:
Student Materials = crayons or markers, pencils, paper.

Teacher Materials = Chalkboard, chalk

ACTIVITIES AND PROCEDURES:

1. Divide the class into groups of four.

2. Each group will receive a number of sheets of paper (24, 25, 26, 27, etc) and they will try to divide equally to each student the same no. of sheets.

3. Ask the groups how do they think that this action can be represented mathematically? After more tries, the teacher and the students will write on the chalkboard the divisions: 24:4=6, 25:4=6 and 1 as remainder, etc. The remainder can be seen as the number of sheets of paper remained.

4. Then take the one paper remained from the second group, cut it in 4 equal parts and then write on the chalk board 25:4=6 and ¼, or 6,25.

The students can learn the division in the following form: 25:4=6,25
24
=10
8
20
20
==
5. Repeat the same thing with the other operations from all the groups in the classroom and make sure that the students have understood both interpretations of these divisions.

6. Teach the students to check the correctness of the division: 25=4 x 6 +1 or 25 = 4 x 6,25.

7. Challenge the students to approximate results of some divisions (for example: 807: 20 is approx. 40 because 807:20 = (800 + 7):20 = 800: 20 + 7: 20 = 40 + 0,35 (distributive) . Another example could be 870:20 = (900-30):20=900:20 – 30:20 = 45 – 1,5= 43,5.

TYING IT ALL TOGETHER:
This lesson can be completed as one lesson or extended to several,
depending on the level and ability of the class. Examples and exercise as many as possible are recommended.

Learning the divisibility rules was my first acknowledgment about how fun and challenging math can be. I was 10 years old and I could have “discover” for my self why a number is divisible by some specific numbers.

Our teacher has written on the board a row of numbers and then he has asked us which ones we think are dividing by 2, then by 5, 10, 100, 3, 9, 25, etc. So, we have found together the right answers and
then it came a more “tricky” question: what do you notice at the numbers divisible by 3? There were numbers like: 9, 21, 36, and 201. And this was my moment of glory! I’ve noticed that the sum of the digits for all these numbers is a multiple of 3 (9 – itself, 2+1=3, 3+6=9, 2+0+1=3). So, all my colleagues have written in their notebooks “MY rule”: a number is dividing by 3 if the sum of its digits is a multiple of 3.

This is an example of the many happy moments of my math classes and I am the proof that what is the more important thing in enjoying a subject is THE TEACHER! The best way to teach is to let the impression to the students that they are discovering math’s rules. If my math teacher would have been taught history, then today I would be a history teacher instead of math teacher. After years, I could see also the lesson plans of my teacher: very complete, done with hard work and love!

This is the kind of lesson plan we want to present you in our next materials. We want them to be helpful and joyful as well. I’m looking forward to hear your opinions and suggestions!

The graphic is really explicit and friendly, the information is presented in a very well organized way and there are simple and precise presentation and examples. The subjects are amazed complete presented, respecting a logical order and – very important! – The curriculum. You can see from the list of the supervisors of this book that this work is a serious project designated to students, parents and teachers interested in achieving a quality and pleasant math education.

Anyone who is interested in a specific subject can easy get to it using the table of contents at the beginning of the book or the index at the end of it.

Each subject is presented with explanations, examples in written and graphical form. Numeration, number theory, computation, statistics, probability and odds are some of the classical math subjects we can study, but there are also some “rarely” chapters as: Problem Solving – strategies/skills, Study Tips, Using a computer for math (spreadsheets, internet), Test Taking Skills.

It’s a very helpful book in making the homework – for student and parent – because it helps each of them to remember easily what they have heard and studied already, but also for the teacher – who can learn different strategies and tips for teaching successfully and can have an overview on the taught subject.

It is a book which makes everyone interested in math feeling more secure and friendly in the “relationship” with mathematics.

It contains seven main themes, a wonderful game “Lions and tigers” for two players, and of course, the answers at the end. All of them are friendly and funny presented; contain lovely stickers and tempting exercises and games to solve and fill-in.

The themes are: Fun and Games (simple and more complicated calculations), Number patterns, 2-D and 3-D shapes, Averages, Timing, Charts and graphs and Fractions. The subjects of the exercises are related to the real life and make them very approachable. We can virtually play badminton, tennis or table tennis, take a walk in the sand, make a camp fire, stay in tents, phone, organize a trip, ride and feed ponies, but also color shapes for real.

I am kindly recommending you this book as an educative extra school activity with your children, which you can use home, but also in holidays during a rainy day… Let me know how much you have enjoyed it.

Divisors, multiples, fractions, decimals, percents, equations become friendly terms coming together with themes like shopping, friends, necklace, lipstick, shoes, boyfriend, love, superstar, eBay – everything what a girl (especially if she is in her middle school years) has interest into.  

The author is a lovely educated actress – one of the models we need for our children.

As a teacher: I wouldn’t hesitate to use it as guide – see the teaching method of the prime numbers/factors – it’s really nice! As a student: this book would be one of my smart and cute friends – see the graphic and the examples, as a parent: I would love to practice and discuss about it together with my daughter.

For my son, I would look for another book… J