DIVISIBILITY

DIVISIBILITY

• SUBJECT: MATHS

• LEVEL/COURSE: 1^st ESO

• LEARNING OUTCOMES:

1. To use natural numbers, their operations and properties to collect, transform and exchange information and solve problems related to daily life: To identify natural numbers and to use them to adequately represent and interpret quantitative information; To calculate the value of numerical expressions of natural numbers through elementary operations and powers of natural exponent by correctly applying the hierarchy of operations; To use properly the natural numbers and their operations, to solve contextualized daily problems.

2. To Know and use properties and new meanings of numbers in contexts of parity, divisibility and elementary operations, thus improving the understanding of the concept of natural numbers: To apply the criteria of divisibility by 2, 3, 5, 9 and 11 to decompose into prime factors natural numbers and to use them in exercises, activities and contextualized problems; To identify and calculate the maximum common divisor and the least common multiple of two or more natural numbers by means of the appropriate algorithm and to apply it to contextualized problems; To carry out calculations involving powers of natural exponent and to apply the basic rules of operations with powers.

• SUBJECT CONTENTS:

1. Natural numbers. Powers of natural exponent

2. .Divisibility of natural numbers. Multiples and divisors. Criteria of divisibility.

3. Prime and compound numbers. Decomposition of a number in prime factors.

4. Common multiples and divisors to several numbers. Maximum common divisor and least common multiple of two or more natural numbers.

• TASKS:

1. Task 1: Class-Group task. To create a memory game of matching cards from terms related to divisibility that will be shown later in the classroom as an English-Spanish divisibility dictionary.

2. Final task (Project): Small group task. To design and build, with the help of the concepts of maximum common factor and least common multiple, two Christmas tree ornaments of cubic shape and two cubed boxes to store them, making the most of the used materials.

• CLASS DISTRIBUTION/ TIMING:

The unit will be developed in 8 sessions of 55 minutes.

• 1st Session:

• Activity 1:

1. Brainstorm in big group about useful vocabulary and expressions of divisibility (multiple, divisor, factor, prime, composite, even, odd, factor into, factorize, HCF, LCM…) and revision of reused vocabulary (operations, powers, cube, square, rectangle,…)

2. To create altogether the necessary glossary to carry out task1.

3. Task 1: Work in pairs. Distribute the terms of the glossary among pairs (one or two terms or expressions for couple). Create a memory game with flash-cards that match each term in English with its meaning in Spanish. Print the flash-cards, cut them and glue them on squares of cardboard. They can be used as materials and resources:

• Class material: carboard, scissors, glue.

• http://www.amathsdictionaryforkids.com/dictionary.html

• http://www.wordreference.com/es/translation.asp

• http://www.scholastic.com/parents/resources/game/tools/flash-card-maker

• Pupil's laptops/tablets

• Printer.

• 2nd Session:

• Activity 2: (15 minutes)

Play the memory game in 4-pupils groups. To distribute 5 pairs of Spanish-English terms among the students. Put them flipped over forming a square and play the typical memory game. Rotate the terms between groups of pupils. The player who takes less time to associate each term with its translation will win in his/her group.

At the end of the game, we will hang the flash-cards in a visible wall in the classroom as a divisibility dictionary.

• Activity 3:

Exposure of the basic contents (multiples and divisors, prime and composite numbers, divisibility rules, prime factors decomposition) through viewing some of the following videos on the class digital board.

• https://www.youtube.com/watch?v=PL8pH1hThHo : 3 minutes explanatory video in English about multiples and divisors.

• https://www.youtube.com/watch?v=TXDyU5f5WR8: 4 minutes explanatory video in English about prime and composite numbers.

• https://www.youtube.com/watch?v=UZYpOKtylxM o https://www.youtube.com/watch?v=Y1pAKJ4rf-M: 5-6 minutes explanatory videos in English about divisibility rules.

• https://www.youtube.com/watch?v=tW97UU01ShY: 6 minutes explanatory vídeo explicativo about factoring numbers using factor trees.

• https://www.youtube.com/watch?v=7EqS71lgvl4 : 4 minutes explanatory video explicativo de 4 minutos about factor numbers into primes.

• 3rd Session:

• Activity 4:

To do individually the activities and exercises that appear in the following links. These activities are proposed to practice the concepts learned. Each pupil will use his/her laptop/tablet to do them.

Activities will be shown on the digital board to help pupils if necessary.

• https://learningapps.org/1828982 :interactive activity to review vocabulary

• https://learningapps.org/1831461, https://es.educaplay.com/es/recursoseducativos/1293852/divisibility_rules_quiz.htm interactive activities to practice divisibility rules.

• https://www.homeschoolmath.net/online/factoring.php : interactive games to practise online the divisibility learned contents.

• https://learningapps.org/display?v=pw4ic7y0t17 : alphabet soup to revise vocabulary.

• https://learningapps.org/display?v=pyvodgpbt17 : clasifying in primes and composite numbers.

• https://learningapps.org/display?v=pfh6e7pr317 : decomposition into primes

• 4th Session:

• Activity 5:

1. Exposure of the concepts of high common factor and least common multiple through viewing the following videos on the class digital board.

• https://www.youtube.com/watch?v=fRoWMakrIhw : Vídeo explicativo sobre cómo hallar el mínimo común múltiplo de dos números a partir de su descomposición factorial (4-5 minutos).

• https://www.youtube.com/watch?v=NtkjbVb3Zv8 : Vídeo sobre cómo hallar el máximo común divisor de dos números a partir de la descomposición factorial de

• https://www.homeschoolmath.net/online/factoring.php actividades interactivas online para practicar el cálculo de m.c.d. y m.c.m.

2. Practice of the calculation algorithm of the HCF and LCM through the factorial decomposition. Pupils must work in pairs but fill in the work-sheet given individually.

3. Do one more review activity following the link:

• https://www.khanacademy.org/math/pre-algebra/pre-algebra-factors-

  multiples/pre-algebra-greatest-common-divisor/e/gcf-and-lcm-word-problems : contextualized word problems using HCF and LCM.

• 5th Session:

• Activity 6:

Access to the eScholarium educational platform and do individually the activities proposed in the digital book "Maths activities with eScholarium / Unit: Divisibility"(*). These activities will be useful as self-evaluation for pupils and as the first test evaluation. Each pupil will use his/her laptop/tablet to do them. Done activities and marks obtained by each pupil will be available for the teacher in eScholarium.

• https://escholarium.educarex.es/LMS/login2.php

  (* )During the 2017-2018 academic year, the Mathematics Department of the IES Gabriel y Galán in Montehermoso participates in a working group to create their own materials with eScholarium for 1st and 2nd courses of ESO. The activities of this unit can be found in the digital book created by the department for 1st course of ESO at the end of this working group.

• 6th Session/ 7th Session:

• Final project:

Distribute the class in 4-5-pupils groups and give them the final task sheet and the necessary materials.

• 8th Session:

  Oral presentation of projects to class group. Digital board will be available to show groups Power Point presentations.

• EVALUATION FINAL WRITTEN EXAM:

https://drive.google.com/a/educarex.es/file/d/1yrrHgz4E7pS0cRHOyW2V-_DFwn781e6N/view?usp=sharing

• EVALUATION RUBRIC:

	ALWAYS	ALMOST ALWAYS	SOMETIMES	RARELY	NEVER
He/She can calculate multiples of a natural number
He/She can calculate all divisors of a natural number
He/She distinguishes prime and composite numbers
He/She apply divisibility rules
He/She factor natural numbers into primes
He/She calculate HCF of two natural numbers
He/She calculate LCM of two natural numbers
He/She solve word contextualized problems using múltiples, divisors, HCF or LCM
He/She can communicate properly in English
He/She is a good team-worker
He/ She surfs the web without difficulty and master the IT tools necessary for the unit activities

Template to design the AICLE didactic unit: https://drive.google.com/a/educarex.es/file/d/1NZWv5TrPAvM3SfB5bBd4Vh9oUaedFT2b/view?usp=sharing

AUTORA: Carolina Sánchez Iglesias

Consejería de Educación y Empleo

Junta de Extremadura