Session Guide for Real Numbers

Real Numbers SESSION GUIDE

Author: Maribel Perez 1

Grade 7 (Grade Level Stadards)

Content / Content Standard

Performance Standard

Learning Competencies

The learner demonstrates understanding of key concepts and principles of number sense, measurement, algebra, geometry, probability and statistics as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decisions in real life.

Numbers and Number Sense

The learner demonstrates understanding of the key concepts of sets, the real number system, estimation / approximation of a square of a number and the measures of quantities, and the applications of real numbers to measurements.

The learner is able to explore set concepts and set operations.

The learner describes and illustrates well-defined sets, subsets, universal set and the null set. defines and describes the union and intersection of sets and the complement of a set. uses Venn Diagrams to represent sets, subsets and set operations. solves problems involving sets. describes and illustrates the absolute value of a number on a number line as the

distance of the number from 0. performs fundamental operations on integers: addition, subtraction, multiplication,

division. states and illustrates the different properties of the operations on integers (commutative,

associative, distributive, identity, inverse). defines and illustrates rational numbers and arrange them on a number line. expresses rational numbers terminating and repeating and non-terminating) from fraction form to decimal form and vice versa performs operations on rational numbers and illustrate their properties. describes principal roots and tells whether they are rational or irrational. determines between what two integers the square root of a number is. estimates the square root of a number to the nearest tenth. illustrates and graphs irrational numbers (square roots) on a number line with and

without appropriate technology. describes, represents and compares the different subsets of real numbers. finds the union, intersection and complement of the set of real numbers and its subsets. arranges real numbers in increasing or decreasing order. determines the significant digits in a given situation. writes very large or very small numbers in scientific notation. describes and represents real-life situations which involve integers, rational numbers,

square roots of a rational numbers and irrational numbers. solves problems involving real numbers.



I. Title: REAL NUMBERS II. Overview: This session deals with competencies on real numbers that will be

discussed/covered in Grade 7 of the K to 12 Curriculum. Discussions are focused on models that can be used as springboard for discussing the procedures for the operations on integers, students common misconceptions about rational numbers, activities/strategies in dealing with irrational

numbers, absolute value, subsets of real numbers and problems on real numbers III. Objectives:

1. Discuss the importance of using models for operations on integers before coming up with

the procedures/rules for these operations. 2. Discuss on students common misconceptions and difficulties in learning about rational numbers and come up with strategies on how to address them.

3. Acquaint the participants on the different activities and how lessons were developed in the learning guides particularly on roots and irrational numbers, absolute value and subsets of real numbers

4. Develop other activities that would help assess students knowledge, processes/skills, understanding, products/performances relating to real numbers.

IV. Materials: manila paper pentel pen number cards sheets of paper

masking tape V. Activities:

A. Operations on Integers Divide the participants into six groups. For each group assign a task and have each group

present their work.

TASK: Illustrate how you are going to add the following integers using the numberline.

1. 7 + 4 2. ( ) ( )36 + 3. ( )78 + 4. ( )125 +

TASK: Illustrate how you are going to add the following integers using counters or signed tiles.

1. 7 + 4 2. ( ) ( )36 + 3. ( )78 + 4. ( )125 +

TASK: Illustrate how you are going to subtract the following integers using the numberline.

1. 38 2. ( ) ( )25 3. 106 4. ( ) 43

TASK: Illustrate how you are going to subtract the following integers using counters.

1. 38 2. ( ) ( )25 3. 106 4. ( ) 43



B. Properties of the Operations on Integers

Ask the participants to do Activity 2 of the TG.

C. Rational Numbers

Prepare rational number cards.

Show the number cards one at a time and ask the participants to put the number in a sentence. Example: Show the number card Ask the participants: Can you use this number in a sentence that has something to do with what you might find in the market or store?

D. Properties of Operations on Rational Numbers

Ask the participants to do the first Activity in the TG, Pick a Pair.

E. Principal Roots and Irrational Numbers Ask the participants to form six groups and ask them to think of a situation or a problem where they can introduce the concept of irrational numbers. Have them present their outputs.

12 2.5 3 5.283 32

3

TASK: Illustrate how you are going to find a pattern for multiplying the following integers.

1. 36 2. ( ) 35 3. ( ) ( )35 4. ( )63

TASK: Illustrate how you are going to find a pattern for dividing the following integers.

1. 318 2. ( ) 315 3. ( ) ( )315 4. ( ) 618



VI. Processing of Activities

A. Operations on Integers After the activity, ask the participants to share their experiences or strategies in

teaching addition, subtraction, multiplication and division of integers. In connection to the

activity given, emphasize on the importance of using models like counters, numberline, and patterns in coming up with the procedures for the operations on integers. At this point, aside from the exercises found in the learning guide, ask the

participants to think about other activities where they can assess students understanding of the operations on integers.

B. Properties of Operations on Integers

The given activity may serve as a good springboard in introducing the properties of operations on integers. Lesson 5 also gives suggestions on visualization of these properties to develop conceptual understanding and later on apply them in solving math problems.

C. Rational Numbers and D. Properties of Operations on Rational Numbers

Rational numbers are everywhere. We can actually encounter them in our daily lives and this is what we want our students to realize. After the activity, we could ask them to locate these numbers on the numberline. Lesson 6, 7, 8 and 9 discusses the rational numbers, forms of and operations on

rational numbers and properties of operations. Discuss with the participants the common misconceptions about rational numbers and students difficulties on rational numbers, like those of fractions such as:

Fractions numerators and denominators can be treated as separate whole numbers Failure to find a common denominator when adding or subtracting fractions with

unlike denominators.

Leaving the denominator unchanged in fraction multiplication problems

With this in mind, have the participants brainstorm on strategies and activities to address these misconceptions and difficulties.

E. Principal Roots and Irrational Numbers After the presentation of the group outputs have the participants comment on the

outputs. Go over the activities in Lesson 10 to acquaint them in the different activities in the development of the lesson on irrational numbers and roots.

Note: Since the strand on real numbers consists of a considerable number of learning competencies, the group may go over the activities on presented on the

TG/LG of the following lessons.

11 The Absolute Value of a Number

12 Subsets of Real Numbers

(13) (Significant Digits and the Scientific Notation)

14 More Problems Involving Real Numbers

In addition, participants may be asked to construct sample activities to assess students knowledge, processes/skills, understanding, products/performances relating to real numbers.



VII. Summary

In this session, we went over some suggested activities for the learning competencies under the strand of Real Numbers. In addition, we were also engaged into discussions on common students misconceptions and difficulties in these lessons and shared our best practices to address

these difficulties. Moreover, we also identified activities to help us assess students knowledge, processes/skills, understanding, products/performances relating to real numbers.

VIII. Assessment

Prepare an activity that you can use to assess students understanding, product/performance, relating to any lesson on real numbers.

IX. Assignment Choose a lesson under real numbers, identify a learning difficulty that can be encountered

by Grade 7 students in such lesson and present a strategy/activity that you would use in class to address that difficulty.

Session Guide for Real Numbers

Documents

Transcript of Session Guide for Real Numbers